LMFDB - Embedded newform 507.2.k.k.488.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(80,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.80"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.k (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			488.14
Character	$\chi$	$=$	507.488
Dual form			507.2.k.k.80.14

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0912193 + 0.340435i) q^{2} +(0.839735 + 1.51487i) q^{3} +(1.62448 - 0.937892i) q^{4} +(2.45719 - 2.45719i) q^{5} +(-0.439116 + 0.424061i) q^{6} +(-1.12240 - 0.300747i) q^{7} +(0.965906 + 0.965906i) q^{8} +(-1.58969 + 2.54419i) q^{9} +(1.06066 + 0.612371i) q^{10} +(-1.81140 + 0.485362i) q^{11} +(2.78492 + 1.67330i) q^{12} -0.409539i q^{14} +(5.78573 + 1.65895i) q^{15} +(1.63506 - 2.83201i) q^{16} +(2.95083 + 5.11099i) q^{17} +(-1.01114 - 0.309108i) q^{18} +(1.27519 - 4.75906i) q^{19} +(1.68707 - 6.29623i) q^{20} +(-0.486926 - 1.95284i) q^{21} +(-0.330468 - 0.572388i) q^{22} +(-1.35482 + 2.34662i) q^{23} +(-0.652122 + 2.27433i) q^{24} -7.07560i q^{25} +(-5.18904 - 0.271740i) q^{27} +(-2.10538 + 0.564135i) q^{28} +(-2.32707 - 1.34353i) q^{29} +(-0.0369941 + 2.12099i) q^{30} +(-3.22500 - 3.22500i) q^{31} +(3.75217 + 1.00539i) q^{32} +(-2.25635 - 2.33646i) q^{33} +(-1.47079 + 1.47079i) q^{34} +(-3.49695 + 2.01896i) q^{35} +(-0.196243 + 5.62393i) q^{36} +(0.559232 + 2.08708i) q^{37} +1.73647 q^{38} +4.74684 q^{40} +(1.76159 + 6.57436i) q^{41} +(0.620400 - 0.343904i) q^{42} +(4.80750 - 2.77561i) q^{43} +(-2.48735 + 2.48735i) q^{44} +(2.34538 + 10.1577i) q^{45} +(-0.922459 - 0.247172i) q^{46} +(-2.23192 - 2.23192i) q^{47} +(5.66317 + 0.0987761i) q^{48} +(-4.89284 - 2.82488i) q^{49} +(2.40878 - 0.645431i) q^{50} +(-5.26460 + 8.76202i) q^{51} +2.46136i q^{53} +(-0.380831 - 1.79132i) q^{54} +(-3.25832 + 5.64358i) q^{55} +(-0.793642 - 1.37463i) q^{56} +(8.28020 - 2.06460i) q^{57} +(0.245112 - 0.914771i) q^{58} +(-2.59020 + 9.66677i) q^{59} +(10.9547 - 2.73147i) q^{60} +(1.33134 + 2.30596i) q^{61} +(0.803720 - 1.39208i) q^{62} +(2.54943 - 2.37750i) q^{63} -5.17117i q^{64} +(0.589590 - 0.981273i) q^{66} +(-6.57167 + 1.76087i) q^{67} +(9.58711 + 5.53512i) q^{68} +(-4.69254 - 0.0818465i) q^{69} +(-1.00632 - 1.00632i) q^{70} +(-11.2116 - 3.00415i) q^{71} +(-3.99294 + 0.921953i) q^{72} +(-9.13263 + 9.13263i) q^{73} +(-0.659503 + 0.380764i) q^{74} +(10.7186 - 5.94163i) q^{75} +(-2.39197 - 8.92696i) q^{76} +2.17908 q^{77} +1.10008 q^{79} +(-2.94114 - 10.9765i) q^{80} +(-3.94577 - 8.08894i) q^{81} +(-2.07745 + 1.19942i) q^{82} +(-4.58922 + 4.58922i) q^{83} +(-2.62256 - 2.71567i) q^{84} +(19.8095 + 5.30793i) q^{85} +(1.38345 + 1.38345i) q^{86} +(0.0811644 - 4.65342i) q^{87} +(-2.21845 - 1.28082i) q^{88} +(-4.12834 + 1.10619i) q^{89} +(-3.24410 + 1.72503i) q^{90} +5.08271i q^{92} +(2.17732 - 7.59361i) q^{93} +(0.556230 - 0.963419i) q^{94} +(-8.56055 - 14.8273i) q^{95} +(1.62779 + 6.52833i) q^{96} +(3.17506 - 11.8495i) q^{97} +(0.515368 - 1.92338i) q^{98} +(1.64471 - 5.38010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) $ 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.0912193	+	0.340435i	0.0645018	+	0.240724i	0.990648	−	0.136440i	$-0.0435660\pi$
$2$	0.0912193	+	0.340435i	0.0645018	+	0.240724i	−0.926147	+	0.377164i	$0.876899\pi$
$3$	0.839735	+	1.51487i	0.484821	+	0.874613i
$3$	0.839735	+	1.51487i	0.484821	+	0.874613i
$4$	1.62448	−	0.937892i	0.812238	−	0.468946i
$5$	2.45719	−	2.45719i	1.09889	−	1.09889i	0.104350	−	0.994541i	$-0.466724\pi$
$5$	2.45719	−	2.45719i	1.09889	−	1.09889i	0.994541	−	0.104350i	$-0.0332761\pi$
$6$	−0.439116	+	0.424061i	−0.179269	+	0.173122i
$7$	−1.12240	−	0.300747i	−0.424228	−	0.113672i	0.0403875	−	0.999184i	$-0.487141\pi$
$7$	−1.12240	−	0.300747i	−0.424228	−	0.113672i	−0.464615	+	0.885513i	$0.653807\pi$
$8$	0.965906	+	0.965906i	0.341499	+	0.341499i
$9$	−1.58969	+	2.54419i	−0.529897	+	0.848062i
$10$	1.06066	+	0.612371i	0.335410	+	0.193649i
$11$	−1.81140	+	0.485362i	−0.546156	+	0.146342i	−0.521339	−	0.853350i	$-0.674567\pi$
$11$	−1.81140	+	0.485362i	−0.546156	+	0.146342i	−0.0248176	+	0.999692i	$0.507900\pi$
$12$	2.78492	+	1.67330i	0.803936	+	0.483039i
$13$		0			0
$13$		0			0
$14$		−	0.409539i		−	0.109454i
$15$	5.78573	+	1.65895i	1.49387	+	0.428339i
$16$	1.63506	−	2.83201i	0.408766	−	0.708003i
$17$	2.95083	+	5.11099i	0.715682	+	1.23960i	0.962696	+	0.270586i	$0.0872174\pi$
$17$	2.95083	+	5.11099i	0.715682	+	1.23960i	−0.247014	+	0.969012i	$0.579449\pi$
$18$	−1.01114	−	0.309108i	−0.238328	−	0.0728573i
$19$	1.27519	−	4.75906i	0.292548	−	1.09180i	−0.650598	−	0.759423i	$-0.725482\pi$
$19$	1.27519	−	4.75906i	0.292548	−	1.09180i	0.943145	−	0.332381i	$-0.107852\pi$
$20$	1.68707	−	6.29623i	0.377240	−	1.40788i
$21$	−0.486926	−	1.95284i	−0.106256	−	0.426146i
$22$	−0.330468	−	0.572388i	−0.0704561	−	0.122034i
$23$	−1.35482	+	2.34662i	−0.282500	+	0.489305i	−0.972000	−	0.234981i	$-0.924497\pi$
$23$	−1.35482	+	2.34662i	−0.282500	+	0.489305i	0.689500	+	0.724286i	$0.257831\pi$
$24$	−0.652122	+	2.27433i	−0.133114	+	0.464246i
$25$		−	7.07560i		−	1.41512i
$26$		0			0
$27$	−5.18904	−	0.271740i	−0.998632	−	0.0522964i
$28$	−2.10538	+	0.564135i	−0.397880	+	0.106612i
$29$	−2.32707	−	1.34353i	−0.432125	−	0.249488i	0.268126	−	0.963384i	$-0.413596\pi$
$29$	−2.32707	−	1.34353i	−0.432125	−	0.249488i	−0.700252	+	0.713896i	$0.746929\pi$
$30$	−0.0369941	+	2.12099i	−0.00675416	+	0.387239i
$31$	−3.22500	−	3.22500i	−0.579227	−	0.579227i	0.355463	−	0.934690i	$-0.384323\pi$
$31$	−3.22500	−	3.22500i	−0.579227	−	0.579227i	−0.934690	+	0.355463i	$0.884323\pi$
$32$	3.75217	+	1.00539i	0.663296	+	0.177730i
$33$	−2.25635	−	2.33646i	−0.392781	−	0.406726i
$34$	−1.47079	+	1.47079i	−0.252238	+	0.252238i
$35$	−3.49695	+	2.01896i	−0.591092	+	0.341267i
$36$	−0.196243	+	5.62393i	−0.0327072	+	0.937321i
$37$	0.559232	+	2.08708i	0.0919372	+	0.343114i	0.996537	−	0.0831470i	$-0.0264971\pi$
$37$	0.559232	+	2.08708i	0.0919372	+	0.343114i	−0.904600	+	0.426261i	$0.859830\pi$
$38$	1.73647			0.281693
$39$		0			0
$40$	4.74684			0.750541
$41$	1.76159	+	6.57436i	0.275115	+	1.02674i	0.955764	+	0.294133i	$0.0950309\pi$
$41$	1.76159	+	6.57436i	0.275115	+	1.02674i	−0.680650	+	0.732609i	$0.738302\pi$
$42$	0.620400	−	0.343904i	0.0957298	−	0.0530655i
$43$	4.80750	−	2.77561i	0.733136	−	0.423276i	−0.0864321	−	0.996258i	$-0.527547\pi$
$43$	4.80750	−	2.77561i	0.733136	−	0.423276i	0.819568	+	0.572981i	$0.194213\pi$
$44$	−2.48735	+	2.48735i	−0.374982	+	0.374982i
$45$	2.34538	+	10.1577i	0.349629	+	1.51423i
$46$	−0.922459	−	0.247172i	−0.136009	−	0.0364436i
$47$	−2.23192	−	2.23192i	−0.325559	−	0.325559i	0.525336	−	0.850895i	$-0.323940\pi$
$47$	−2.23192	−	2.23192i	−0.325559	−	0.325559i	−0.850895	+	0.525336i	$0.823940\pi$
$48$	5.66317	+	0.0987761i	0.817408	+	0.0142571i
$49$	−4.89284	−	2.82488i	−0.698977	−	0.403555i
$50$	2.40878	−	0.645431i	0.340653	−	0.0912777i
$51$	−5.26460	+	8.76202i	−0.737191	+	1.22693i
$52$		0			0
$53$			2.46136i			0.338093i	0.985608	+	0.169047i	$0.0540689\pi$
$53$			2.46136i			0.338093i	−0.985608	+	0.169047i	$0.945931\pi$
$54$	−0.380831	−	1.79132i	−0.0518245	−	0.243768i
$55$	−3.25832	+	5.64358i	−0.439352	+	0.760980i
$56$	−0.793642	−	1.37463i	−0.106055	−	0.183692i
$57$	8.28020	−	2.06460i	1.09674	−	0.273463i
$58$	0.245112	−	0.914771i	0.0321848	−	0.120115i
$59$	−2.59020	+	9.66677i	−0.337216	+	1.25851i	0.564231	+	0.825617i	$0.309173\pi$
$59$	−2.59020	+	9.66677i	−0.337216	+	1.25851i	−0.901447	+	0.432890i	$0.857494\pi$
$60$	10.9547	−	2.73147i	1.41424	−	0.352631i
$61$	1.33134	+	2.30596i	0.170461	+	0.295247i	0.938581	−	0.345058i	$-0.112141\pi$
$61$	1.33134	+	2.30596i	0.170461	+	0.295247i	−0.768120	+	0.640306i	$0.778808\pi$
$62$	0.803720	−	1.39208i	0.102073	−	0.176795i
$63$	2.54943	−	2.37750i	0.321198	−	0.299537i
$64$		−	5.17117i		−	0.646397i
$65$		0			0
$66$	0.589590	−	0.981273i	0.0725736	−	0.120786i
$67$	−6.57167	+	1.76087i	−0.802857	+	0.215125i	−0.636838	−	0.770998i	$-0.719758\pi$
$67$	−6.57167	+	1.76087i	−0.802857	+	0.215125i	−0.166019	+	0.986123i	$0.553091\pi$
$68$	9.58711	+	5.53512i	1.16261	+	0.671232i
$69$	−4.69254	−	0.0818465i	−0.564915	−	0.00985317i
$70$	−1.00632	−	1.00632i	−0.120278	−	0.120278i
$71$	−11.2116	−	3.00415i	−1.33058	−	0.356527i	−0.477647	−	0.878552i	$-0.658510\pi$
$71$	−11.2116	−	3.00415i	−1.33058	−	0.356527i	−0.852930	+	0.522025i	$0.825177\pi$
$72$	−3.99294	+	0.921953i	−0.470572	+	0.108653i
$73$	−9.13263	+	9.13263i	−1.06889	+	1.06889i	−0.0714492	+	0.997444i	$0.522762\pi$
$73$	−9.13263	+	9.13263i	−1.06889	+	1.06889i	−0.997444	+	0.0714492i	$0.977238\pi$
$74$	−0.659503	+	0.380764i	−0.0766657	+	0.0442630i
$75$	10.7186	−	5.94163i	1.23768	−	0.686080i
$76$	−2.39197	−	8.92696i	−0.274378	−	1.02399i
$77$	2.17908			0.248330
$78$		0			0
$79$	1.10008			0.123769			0.0618844	−	0.998083i	$-0.480289\pi$
$79$	1.10008			0.123769			0.0618844	+	0.998083i	$0.480289\pi$
$80$	−2.94114	−	10.9765i	−0.328829	−	1.22721i
$81$	−3.94577	−	8.08894i	−0.438419	−	0.898771i
$82$	−2.07745	+	1.19942i	−0.229416	+	0.132453i
$83$	−4.58922	+	4.58922i	−0.503732	+	0.503732i	−0.912596	−	0.408864i	$-0.865925\pi$
$83$	−4.58922	+	4.58922i	−0.503732	+	0.503732i	0.408864	+	0.912596i	$0.365925\pi$
$84$	−2.62256	−	2.71567i	−0.286144	−	0.296303i
$85$	19.8095	+	5.30793i	2.14864	+	0.575726i
$86$	1.38345	+	1.38345i	0.149181	+	0.149181i
$87$	0.0811644	−	4.65342i	0.00870173	−	0.498899i
$88$	−2.21845	−	1.28082i	−0.236488	−	0.136536i
$89$	−4.12834	+	1.10619i	−0.437604	+	0.117256i	−0.470893	−	0.882190i	$-0.656068\pi$
$89$	−4.12834	+	1.10619i	−0.437604	+	0.117256i	0.0332896	+	0.999446i	$0.489402\pi$
$90$	−3.24410	+	1.72503i	−0.341959	+	0.181834i
$91$		0			0
$92$			5.08271i			0.529909i
$93$	2.17732	−	7.59361i	0.225778	−	0.787421i
$94$	0.556230	−	0.963419i	0.0573708	−	0.0993691i
$95$	−8.56055	−	14.8273i	−0.878294	−	1.52125i
$96$	1.62779	+	6.52833i	0.166135	+	0.666295i
$97$	3.17506	−	11.8495i	0.322379	−	1.20313i	−0.594542	−	0.804065i	$-0.702667\pi$
$97$	3.17506	−	11.8495i	0.322379	−	1.20313i	0.916921	−	0.399070i	$-0.130667\pi$
$98$	0.515368	−	1.92338i	0.0520600	−	0.194291i
$99$	1.64471	−	5.38010i	0.165299	−	0.540721i
$100$	−6.63614	−	11.4941i	−0.663614	−	1.14941i
$101$	5.54779	−	9.60905i	0.552026	−	0.956137i	−0.446103	−	0.894982i	$-0.647188\pi$
$101$	5.54779	−	9.60905i	0.552026	−	0.956137i	0.998128	−	0.0611547i	$-0.0194783\pi$
$102$	−3.46313	−	0.992988i	−0.342901	−	0.0983204i
$103$			4.43285i			0.436782i	0.975861	+	0.218391i	$0.0700808\pi$
$103$			4.43285i			0.436782i	−0.975861	+	0.218391i	$0.929919\pi$
$104$		0			0
$105$	−5.99499	−	3.60205i	−0.585051	−	0.351524i
$106$	−0.837932	+	0.224523i	−0.0813872	+	0.0218076i
$107$	−11.3063	−	6.52769i	−1.09302	−	0.631055i	−0.158641	−	0.987336i	$-0.550711\pi$
$107$	−11.3063	−	6.52769i	−1.09302	−	0.631055i	−0.934379	+	0.356281i	$0.884045\pi$
$108$	−8.68434	+	4.42532i	−0.835651	+	0.425827i
$109$	4.48829	+	4.48829i	0.429901	+	0.429901i	0.888594	−	0.458694i	$-0.151682\pi$
$109$	4.48829	+	4.48829i	0.429901	+	0.429901i	−0.458694	+	0.888594i	$0.651682\pi$
$110$	−2.21849	−	0.594443i	−0.211525	−	0.0566780i
$111$	−2.69206	+	2.59976i	−0.255519	+	0.246759i
$112$	−2.68692	+	2.68692i	−0.253890	+	0.253890i
$113$	11.2693	−	6.50632i	1.06012	−	0.612063i	0.134657	−	0.990892i	$-0.457007\pi$
$113$	11.2693	−	6.50632i	1.06012	−	0.612063i	0.925467	+	0.378829i	$0.123673\pi$
$114$	1.45818	+	2.63054i	0.136571	+	0.246372i
$115$	2.43705	+	9.09518i	0.227256	+	0.848130i
$116$	−5.04035			−0.467985
$117$		0			0
$118$	−3.52718			−0.324704
$119$	−1.77491	−	6.62404i	−0.162705	−	0.607225i
$120$	3.98608	+	7.19086i	0.363878	+	0.656433i
$121$	−6.48070	+	3.74164i	−0.589155	+	0.340149i
$122$	−0.663584	+	0.663584i	−0.0600781	+	0.0600781i
$123$	−8.48005	+	8.18931i	−0.764621	+	0.738405i
$124$	−8.26363	−	2.21423i	−0.742096	−	0.198844i
$125$	−5.10014	−	5.10014i	−0.456171	−	0.456171i
$126$	1.04194	+	0.651040i	0.0928236	+	0.0579992i
$127$	−6.74982	−	3.89701i	−0.598950	−	0.345804i	0.169679	−	0.985499i	$-0.445727\pi$
$127$	−6.74982	−	3.89701i	−0.598950	−	0.345804i	−0.768628	+	0.639696i	$0.779060\pi$
$128$	9.26479	−	2.48249i	0.818900	−	0.219423i
$129$	8.24172	+	4.95198i	0.725643	+	0.435997i
$130$		0			0
$131$		−	18.5420i		−	1.62003i	−0.586412	−	0.810013i	$-0.699460\pi$
$131$		−	18.5420i		−	1.62003i	0.586412	−	0.810013i	$-0.300540\pi$
$132$	−5.85674	−	1.67931i	−0.509764	−	0.146165i
$133$	−2.86254	+	4.95807i	−0.248214	+	0.429919i
$134$	−1.19893	−	2.07660i	−0.103571	−	0.179391i
$135$	−13.4182	+	12.0828i	−1.15485	+	1.03992i
$136$	−2.08651	+	7.78697i	−0.178917	+	0.667727i
$137$	−1.95016	+	7.27811i	−0.166614	+	0.621811i	0.831215	+	0.555951i	$0.187646\pi$
$137$	−1.95016	+	7.27811i	−0.166614	+	0.621811i	−0.997829	+	0.0658600i	$0.979021\pi$
$138$	−0.400186	−	1.60497i	−0.0340661	−	0.136624i
$139$	2.69616	+	4.66989i	0.228685	+	0.396095i	0.957419	−	0.288703i	$-0.0932239\pi$
$139$	2.69616	+	4.66989i	0.228685	+	0.396095i	−0.728733	+	0.684798i	$0.759891\pi$
$140$	−3.78714	+	6.55952i	−0.320072	+	0.554381i
$141$	1.50686	−	5.25531i	0.126900	−	0.442577i
$142$		−	4.09087i		−	0.343298i
$143$		0			0
$144$	4.60592	+	8.66193i	0.383827	+	0.721828i
$145$	−9.01937	+	2.41673i	−0.749018	+	0.200699i
$146$	−3.94214	−	2.27600i	−0.326254	−	0.188363i
$147$	0.170655	−	9.78419i	0.0140753	−	0.806987i
$148$	2.86592	+	2.86592i	0.235577	+	0.235577i
$149$	22.0357	+	5.90444i	1.80523	+	0.483710i	0.994775	−	0.102088i	$-0.0325523\pi$
$149$	22.0357	+	5.90444i	1.80523	+	0.483710i	0.810457	+	0.585798i	$0.199219\pi$
$150$	3.00049	+	3.10701i	0.244989	+	0.253686i
$151$	6.61873	−	6.61873i	0.538625	−	0.538625i	−0.384500	−	0.923125i	$-0.625626\pi$
$151$	6.61873	−	6.61873i	0.538625	−	0.538625i	0.923125	+	0.384500i	$0.125626\pi$
$152$	5.82852	−	3.36510i	0.472755	−	0.272945i
$153$	−17.6942	−	0.617428i	−1.43049	−	0.0499161i
$154$	0.198774	+	0.741836i	0.0160177	+	0.0597789i
$155$	−15.8489			−1.27301
$156$		0			0
$157$	15.6785			1.25128			0.625640	−	0.780112i	$-0.284838\pi$
$157$	15.6785			1.25128			0.625640	+	0.780112i	$0.284838\pi$
$158$	0.100349	+	0.374506i	0.00798331	+	0.0297941i
$159$	−3.72865	+	2.06689i	−0.295701	+	0.163915i
$160$	11.6902	−	6.74937i	0.924195	−	0.533584i
$161$	2.22640	−	2.22640i	0.175465	−	0.175465i
$162$	2.39383	−	2.08114i	0.188077	−	0.163510i
$163$	−3.33861	−	0.894579i	−0.261500	−	0.0700688i	0.125687	−	0.992070i	$-0.459887\pi$
$163$	−3.33861	−	0.894579i	−0.261500	−	0.0700688i	−0.387187	+	0.922001i	$0.626553\pi$
$164$	9.02770	+	9.02770i	0.704945	+	0.704945i
$165$	−11.2854	−	0.196839i	−0.878570	−	0.0153239i
$166$	−1.98096	−	1.14371i	−0.153752	−	0.0887687i
$167$	5.06462	−	1.35706i	0.391912	−	0.105012i	−0.0574813	−	0.998347i	$-0.518307\pi$
$167$	5.06462	−	1.35706i	0.391912	−	0.105012i	0.449393	+	0.893334i	$0.351640\pi$
$168$	1.41594	−	2.35659i	0.109242	−	0.181815i
$169$		0			0
$170$			7.22802i			0.554364i
$171$	10.0808	+	10.8097i	0.770897	+	0.826642i
$172$	5.20644	−	9.01782i	0.396987	−	0.687602i
$173$	7.12562	+	12.3419i	0.541751	+	0.938339i	0.998804	+	0.0489001i	$0.0155716\pi$
$173$	7.12562	+	12.3419i	0.541751	+	0.938339i	−0.457053	+	0.889439i	$0.651095\pi$
$174$	1.59159	−	0.396851i	0.120658	−	0.0300852i
$175$	−2.12796	+	7.94166i	−0.160859	+	0.600333i
$176$	−1.58720	+	5.92349i	−0.119639	+	0.446500i
$177$	−16.8190	+	4.19369i	−1.26420	+	0.315217i
$178$	−0.753169	−	1.30453i	−0.0564524	−	0.0977785i
$179$	−2.18334	+	3.78165i	−0.163190	+	0.282654i	−0.936011	−	0.351970i	$-0.885512\pi$
$179$	−2.18334	+	3.78165i	−0.163190	+	0.282654i	0.772821	+	0.634624i	$0.218845\pi$
$180$	13.3369	+	14.3013i	0.994071	+	1.06595i
$181$		−	2.10738i		−	0.156640i	−0.996928	−	0.0783201i	$-0.975044\pi$
$181$		−	2.10738i		−	0.156640i	0.996928	−	0.0783201i	$-0.0249556\pi$
$182$		0			0
$183$	−2.37526	+	3.95321i	−0.175584	+	0.292230i
$184$	−3.57525	+	0.957986i	−0.263571	+	0.0706237i
$185$	6.50251	+	3.75422i	0.478074	+	0.276016i
$186$	2.78375	+	0.0485537i	0.204114	+	0.00356013i
$187$	−7.82581	−	7.82581i	−0.572280	−	0.572280i
$188$	−5.71901	−	1.53240i	−0.417101	−	0.111762i
$189$	5.74246	+	1.86559i	0.417703	+	0.135702i
$190$	4.26685	−	4.26685i	0.309550	−	0.309550i
$191$	−5.88706	+	3.39890i	−0.425973	+	0.245935i	−0.697629	−	0.716459i	$-0.745762\pi$
$191$	−5.88706	+	3.39890i	−0.425973	+	0.245935i	0.271657	+	0.962394i	$0.412428\pi$
$192$	7.83368	−	4.34242i	0.565347	−	0.313387i
$193$	−2.87709	−	10.7374i	−0.207098	−	0.772898i	−0.988800	−	0.149247i	$-0.952315\pi$
$193$	−2.87709	−	10.7374i	−0.207098	−	0.772898i	0.781702	−	0.623652i	$-0.214352\pi$
$194$	4.32361			0.310417
$195$		0			0
$196$	−10.5977			−0.756981
$197$	0.591102	+	2.20602i	0.0421143	+	0.157173i	0.983781	−	0.179375i	$-0.0574074\pi$
$197$	0.591102	+	2.20602i	0.0421143	+	0.157173i	−0.941667	+	0.336547i	$0.890741\pi$
$198$	1.98160	+	0.0691468i	0.140826	+	0.00491405i
$199$	−15.8856	+	9.17157i	−1.12610	+	0.650155i	−0.942952	−	0.332930i	$-0.891963\pi$
$199$	−15.8856	+	9.17157i	−1.12610	+	0.650155i	−0.183150	+	0.983085i	$0.558629\pi$
$200$	6.83436	−	6.83436i	0.483262	−	0.483262i
$201$	−8.18597	−	8.47659i	−0.577393	−	0.597893i
$202$	3.77732	+	1.01213i	0.265772	+	0.0712133i
$203$	2.20784	+	2.20784i	0.154960	+	0.154960i
$204$	−0.334383	+	19.1713i	−0.0234115	+	1.34226i
$205$	20.4830	+	11.8259i	1.43060	+	0.825956i
$206$	−1.50910	+	0.404361i	−0.105144	+	0.0281732i
$207$	−3.81650	−	7.17733i	−0.265265	−	0.498859i
$208$		0			0
$209$			9.23947i			0.639107i
$210$	0.679404	−	2.36948i	0.0468833	−	0.163510i
$211$	4.00362	−	6.93447i	0.275620	−	0.477388i	−0.694671	−	0.719327i	$-0.744450\pi$
$211$	4.00362	−	6.93447i	0.275620	−	0.477388i	0.970291	+	0.241939i	$0.0777834\pi$
$212$	2.30849	+	3.99842i	0.158548	+	0.274612i
$213$	−4.86389	−	19.5069i	−0.333269	−	1.33659i
$214$	1.19090	−	4.44451i	0.0814084	−	0.303820i
$215$	4.99274	−	18.6332i	0.340502	−	1.27077i
$216$	−4.74965	−	5.27460i	−0.323173	−	0.358891i
$217$	2.64984	+	4.58965i	0.179883	+	0.311566i
$218$	−1.11855	+	1.93739i	−0.0757580	+	0.131217i
$219$	−21.5038	−	6.16580i	−1.45309	−	0.416646i
$220$			12.2238i			0.824129i
$221$		0			0
$222$	−1.13062	−	0.679324i	−0.0758821	−	0.0455932i
$223$	27.3497	−	7.32834i	1.83147	−	0.490742i	0.833393	−	0.552680i	$-0.186395\pi$
$223$	27.3497	−	7.32834i	1.83147	−	0.490742i	0.998080	+	0.0619383i	$0.0197282\pi$
$224$	−3.90907	−	2.25691i	−0.261186	−	0.150796i
$225$	18.0016	+	11.2480i	1.20011	+	0.749867i
$226$	3.24295	+	3.24295i	0.215718	+	0.215718i
$227$	−7.10455	−	1.90366i	−0.471546	−	0.126350i	0.0152176	−	0.999884i	$-0.495156\pi$
$227$	−7.10455	−	1.90366i	−0.471546	−	0.126350i	−0.486763	+	0.873534i	$0.661823\pi$
$228$	11.5146	−	11.1198i	0.762574	−	0.736428i
$229$	11.4094	−	11.4094i	0.753951	−	0.753951i	−0.221263	−	0.975214i	$-0.571018\pi$
$229$	11.4094	−	11.4094i	0.753951	−	0.753951i	0.975214	+	0.221263i	$0.0710179\pi$
$230$	−2.87401	+	1.65931i	−0.189507	+	0.109412i
$231$	1.82985	+	3.30104i	0.120395	+	0.217192i
$232$	−0.950001	−	3.54545i	−0.0623706	−	0.232770i
$233$	18.1554			1.18940			0.594700	−	0.803947i	$-0.297271\pi$
$233$	18.1554			1.18940			0.594700	+	0.803947i	$0.297271\pi$
$234$		0			0
$235$	−10.9685			−0.715508
$236$	4.85866	+	18.1328i	0.316272	+	1.18034i
$237$	0.923776	+	1.66648i	0.0600057	+	0.108250i
$238$	2.09315	−	1.20848i	0.135679	−	0.0783341i
$239$	6.54262	−	6.54262i	0.423207	−	0.423207i	−0.463099	−	0.886306i	$-0.653263\pi$
$239$	6.54262	−	6.54262i	0.423207	−	0.423207i	0.886306	+	0.463099i	$0.153263\pi$
$240$	14.1582	−	13.6728i	0.913908	−	0.882574i
$241$	−26.7340	−	7.16336i	−1.72209	−	0.461433i	−0.743754	−	0.668453i	$-0.766957\pi$
$241$	−26.7340	−	7.16336i	−1.72209	−	0.461433i	−0.978337	+	0.207021i	$0.933623\pi$
$242$	−1.86495	−	1.86495i	−0.119883	−	0.119883i
$243$	8.94033	−	12.7699i	0.573522	−	0.819190i
$244$	4.32547	+	2.49731i	0.276910	+	0.159874i
$245$	−18.9639	+	5.08137i	−1.21156	+	0.324637i
$246$	−3.56147	−	2.13988i	−0.227071	−	0.136434i
$247$		0			0
$248$		−	6.23009i		−	0.395611i
$249$	−10.8058	−	3.09836i	−0.684791	−	0.196351i
$250$	1.27104	−	2.20150i	0.0803874	−	0.139235i
$251$	2.80003	+	4.84979i	0.176736	+	0.306116i	0.940761	−	0.339071i	$-0.110113\pi$
$251$	2.80003	+	4.84979i	0.176736	+	0.306116i	−0.764025	+	0.645187i	$0.776779\pi$
$252$	1.91164	−	6.25328i	0.120422	−	0.393920i
$253$	1.31516	−	4.90825i	0.0826834	−	0.308579i
$254$	0.710965	−	2.65336i	0.0446099	−	0.166486i
$255$	8.59385	+	34.4661i	0.538168	+	2.15835i
$256$	−3.48092	−	6.02913i	−0.217557	−	0.376821i
$257$	3.40679	−	5.90073i	0.212510	−	0.368077i	−0.739990	−	0.672618i	$-0.765170\pi$
$257$	3.40679	−	5.90073i	0.212510	−	0.368077i	0.952499	+	0.304541i	$0.0985030\pi$
$258$	−0.934023	+	3.25749i	−0.0581497	+	0.202802i
$259$		−	2.51073i		−	0.156009i
$260$		0			0
$261$	7.11751	−	3.78469i	0.440563	−	0.234266i
$262$	6.31236	−	1.69139i	0.389979	−	0.104495i
$263$	19.5996	+	11.3159i	1.20857	+	0.697765i	0.962446	−	0.271474i	$-0.0875111\pi$
$263$	19.5996	+	11.3159i	1.20857	+	0.697765i	0.246119	+	0.969240i	$0.420844\pi$
$264$	0.0773761	−	4.43623i	0.00476217	−	0.273031i
$265$	6.04803	+	6.04803i	0.371528	+	0.371528i
$266$	−1.94902	−	0.522238i	−0.119502	−	0.0320205i
$267$	−5.14245	−	5.32502i	−0.314713	−	0.325886i
$268$	−9.02401	+	9.02401i	−0.551229	+	0.551229i
$269$	−22.6058	+	13.0515i	−1.37830	+	0.795762i	−0.991955	−	0.126593i	$-0.959596\pi$
$269$	−22.6058	+	13.0515i	−1.37830	+	0.795762i	−0.386345	+	0.922354i	$0.626262\pi$
$270$	−5.33739	−	3.46584i	−0.324823	−	0.210925i
$271$	4.57652	+	17.0798i	0.278004	+	1.03753i	0.953801	+	0.300438i	$0.0971328\pi$
$271$	4.57652	+	17.0798i	0.278004	+	1.03753i	−0.675797	+	0.737087i	$0.736201\pi$
$272$	19.2992			1.17019
$273$		0			0
$274$	−2.65562			−0.160432
$275$	3.43423	+	12.8167i	0.207092	+	0.772876i
$276$	−7.69967	+	4.26813i	−0.463466	+	0.256911i
$277$	19.6593	−	11.3503i	1.18122	−	0.681975i	0.224920	−	0.974377i	$-0.427788\pi$
$277$	19.6593	−	11.3503i	1.18122	−	0.681975i	0.956295	+	0.292402i	$0.0944546\pi$
$278$	−1.34385	+	1.34385i	−0.0805989	+	0.0805989i
$279$	13.3317	−	3.07825i	0.798151	−	0.184290i
$280$	−5.32786	−	1.42759i	−0.318400	−	0.0853151i
$281$	−8.55751	−	8.55751i	−0.510498	−	0.510498i	0.404181	−	0.914679i	$-0.367557\pi$
$281$	−8.55751	−	8.55751i	−0.510498	−	0.510498i	−0.914679	+	0.404181i	$0.867557\pi$
$282$	1.92655	+	0.0336025i	0.114724	+	0.00200100i
$283$	6.15361	+	3.55279i	0.365794	+	0.211192i	0.671620	−	0.740896i	$-0.265599\pi$
$283$	6.15361	+	3.55279i	0.365794	+	0.211192i	−0.305825	+	0.952088i	$0.598932\pi$
$284$	−21.0306	+	5.63513i	−1.24794	+	0.334384i
$285$	15.2729	−	25.4192i	0.904690	−	1.50570i
$286$		0			0
$287$		−	7.90886i		−	0.466845i
$288$	−8.52269	+	7.94796i	−0.502205	+	0.468338i
$289$	−8.91483	+	15.4409i	−0.524402	+	0.908291i
$290$	−1.64548	−	2.85006i	−0.0966260	−	0.167361i
$291$	20.6167	−	5.14061i	1.20857	−	0.301348i
$292$	−6.27032	+	23.4012i	−0.366943	+	1.36945i
$293$	4.11392	−	15.3534i	0.240338	−	0.896953i	−0.735332	−	0.677707i	$-0.762974\pi$
$293$	4.11392	−	15.3534i	0.240338	−	0.896953i	0.975670	−	0.219245i	$-0.0703596\pi$
$294$	3.34645	−	0.834411i	0.195169	−	0.0486638i
$295$	17.3885	+	30.1178i	1.01240	+	1.75352i
$296$	−1.47576	+	2.55609i	−0.0857768	+	0.148570i
$297$	9.53130	−	2.02633i	0.553062	−	0.117580i
$298$			8.04031i			0.465763i
$299$		0			0
$300$	11.8396	−	19.7050i	0.683558	−	1.13767i
$301$	−6.23070	+	1.66951i	−0.359131	+	0.0962289i
$302$	2.85701	+	1.64949i	0.164402	+	0.0949176i
$303$	19.2152	+	0.335149i	1.10388	+	0.0192538i
$304$	−11.3927	−	11.3927i	−0.653417	−	0.653417i
$305$	8.93755	+	2.39481i	0.511763	+	0.137126i
$306$	−1.40386	−	6.08006i	−0.0802534	−	0.347574i
$307$	14.3846	−	14.3846i	0.820970	−	0.820970i	−0.165277	−	0.986247i	$-0.552852\pi$
$307$	14.3846	−	14.3846i	0.820970	−	0.820970i	0.986247	+	0.165277i	$0.0528518\pi$
$308$	3.53987	−	2.04374i	0.201703	−	0.116453i
$309$	−6.71521	+	3.72242i	−0.382015	+	0.211761i
$310$	−1.44572	−	5.39552i	−0.0821116	−	0.306445i
$311$	−7.62181			−0.432193			−0.216097	−	0.976372i	$-0.569333\pi$
$311$	−7.62181			−0.432193			−0.216097	+	0.976372i	$0.569333\pi$
$312$		0			0
$313$	−6.51488			−0.368243			−0.184121	−	0.982904i	$-0.558944\pi$
$313$	−6.51488			−0.368243			−0.184121	+	0.982904i	$0.558944\pi$
$314$	1.43018	+	5.33751i	0.0807099	+	0.301213i
$315$	0.422445	−	12.1064i	0.0238021	−	0.682120i
$316$	1.78705	−	1.03176i	0.100530	−	0.0580408i
$317$	−6.29415	+	6.29415i	−0.353515	+	0.353515i	−0.861416	−	0.507901i	$-0.830422\pi$
$317$	−6.29415	+	6.29415i	−0.353515	+	0.353515i	0.507901	+	0.861416i	$0.330422\pi$
$318$	−1.04377	−	1.08082i	−0.0585315	−	0.0606095i
$319$	4.86734	+	1.30420i	0.272518	+	0.0730211i
$320$	−12.7066	−	12.7066i	−0.710319	−	0.710319i
$321$	0.394345	−	22.6091i	0.0220102	−	1.26192i
$322$	0.961034	+	0.554853i	0.0535563	+	0.0309207i
$323$	28.0864	−	7.52572i	1.56277	−	0.418743i
$324$	−13.9963	−	9.43958i	−0.777575	−	0.524421i
$325$		0			0
$326$		−	1.21818i		−	0.0674689i
$327$	−3.03023	+	10.5682i	−0.167572	+	0.584422i
$328$	−4.64868	+	8.05175i	−0.256680	+	0.444583i
$329$	1.83387	+	3.17636i	0.101105	+	0.175118i
$330$	−0.962439	−	3.85991i	−0.0529805	−	0.212481i
$331$	−4.16094	+	15.5288i	−0.228706	+	0.853541i	0.752180	+	0.658958i	$0.229002\pi$
$331$	−4.16094	+	15.5288i	−0.228706	+	0.853541i	−0.980886	+	0.194584i	$0.937664\pi$
$332$	−3.15088	+	11.7593i	−0.172927	+	0.645373i
$333$	−6.19893	−	1.89502i	−0.339699	−	0.103847i
$334$	0.923981	+	1.60038i	0.0505580	+	0.0875690i
$335$	−11.8211	+	20.4747i	−0.645853	+	1.11865i
$336$	−6.32664	−	1.81404i	−0.345146	−	0.0989642i
$337$			28.3556i			1.54463i	0.635243	+	0.772313i	$0.280900\pi$
$337$			28.3556i			1.54463i	−0.635243	+	0.772313i	$0.719100\pi$
$338$		0			0
$339$	19.3195	+	11.6080i	1.04929	+	0.630457i
$340$	37.1583	−	9.95653i	2.01519	−	0.539968i
$341$	7.40704	+	4.27646i	0.401114	+	0.231583i
$342$	−2.76045	+	4.41791i	−0.149268	+	0.238893i
$343$	10.3937	+	10.3937i	0.561209	+	0.561209i
$344$	7.32457	+	1.96261i	0.394914	+	0.105817i
$345$	−11.7316	+	11.3294i	−0.631607	+	0.609952i
$346$	−3.55163	+	3.55163i	−0.190937	+	0.190937i
$347$	−9.59025	+	5.53693i	−0.514831	+	0.297238i	−0.734817	−	0.678265i	$-0.762732\pi$
$347$	−9.59025	+	5.53693i	−0.514831	+	0.297238i	0.219986	+	0.975503i	$0.429399\pi$
$348$	−4.23256	−	7.63550i	−0.226889	−	0.409306i
$349$	7.74319	+	28.8980i	0.414483	+	1.54687i	0.785868	+	0.618394i	$0.212216\pi$
$349$	7.74319	+	28.8980i	0.414483	+	1.54687i	−0.371385	+	0.928479i	$0.621117\pi$
$350$	−2.89773			−0.154890
$351$		0			0
$352$	−7.28464			−0.388273
$353$	−3.28082	−	12.2442i	−0.174620	−	0.651692i	−0.996616	−	0.0821982i	$-0.973806\pi$
$353$	−3.28082	−	12.2442i	−0.174620	−	0.651692i	0.821996	−	0.569494i	$-0.192861\pi$
$354$	−2.96190	−	5.34324i	−0.157423	−	0.283990i
$355$	−34.9309	+	20.1674i	−1.85394	+	1.07037i
$356$	−5.66891	+	5.66891i	−0.300452	+	0.300452i
$357$	8.54414	−	8.25120i	0.452204	−	0.436700i
$358$	−1.48657	−	0.398325i	−0.0785676	−	0.0210521i
$359$	20.3859	+	20.3859i	1.07593	+	1.07593i	0.996870	+	0.0790589i	$0.0251915\pi$
$359$	20.3859	+	20.3859i	1.07593	+	1.07593i	0.0790589	+	0.996870i	$0.474808\pi$
$360$	−7.54600	+	12.0768i	−0.397709	+	0.636505i
$361$	−4.56807	−	2.63738i	−0.240425	−	0.138809i
$362$	0.717426	−	0.192234i	0.0377071	−	0.0101036i
$363$	−11.1102	−	6.67547i	−0.583133	−	0.350371i
$364$		0			0
$365$			44.8813i			2.34919i
$366$	−1.56248	−	0.448012i	−0.0816722	−	0.0234180i
$367$	11.5695	−	20.0389i	0.603922	−	1.04602i	−0.388299	−	0.921533i	$-0.626937\pi$
$367$	11.5695	−	20.0389i	0.603922	−	1.04602i	0.992221	−	0.124490i	$-0.0397295\pi$
$368$	4.43045	+	7.67376i	0.230953	+	0.400023i
$369$	−19.5268	−	5.96937i	−1.01652	−	0.310753i
$370$	−0.684915	+	2.55614i	−0.0356071	+	0.132887i
$371$	0.740245	−	2.76263i	0.0384316	−	0.143429i
$372$	−3.58497	−	14.3777i	−0.185872	−	0.745451i
$373$	−10.2408	−	17.7376i	−0.530249	−	0.918419i	−0.999377	−	0.0352886i	$-0.988765\pi$
$373$	−10.2408	−	17.7376i	−0.530249	−	0.918419i	0.469128	−	0.883130i	$-0.344568\pi$
$374$	1.95031	−	3.37804i	0.100848	−	0.174674i
$375$	3.44331	−	12.0088i	0.177812	−	0.620134i
$376$		−	4.31166i		−	0.222357i
$377$		0			0
$378$	−0.111288	+	2.12511i	−0.00572404	+	0.109304i
$379$	−3.83602	+	1.02786i	−0.197043	+	0.0527975i	−0.355991	−	0.934489i	$-0.615857\pi$
$379$	−3.83602	+	1.02786i	−0.197043	+	0.0527975i	0.158948	+	0.987287i	$0.449190\pi$
$380$	−27.8128	−	16.0577i	−1.42677	−	0.823744i
$381$	0.235423	−	13.4976i	0.0120611	−	0.691502i
$382$	−1.69412	−	1.69412i	−0.0866785	−	0.0866785i
$383$	−25.7044	−	6.88748i	−1.31344	−	0.351934i	−0.466921	−	0.884299i	$-0.654637\pi$
$383$	−25.7044	−	6.88748i	−1.31344	−	0.351934i	−0.846515	+	0.532365i	$0.821303\pi$
$384$	11.5406	+	11.9504i	0.588931	+	0.609839i
$385$	5.35443	−	5.35443i	0.272887	−	0.272887i
$386$	3.39296	−	1.95893i	0.172697	−	0.0997067i
$387$	−0.580765	+	16.6435i	−0.0295219	+	0.846038i
$388$	−5.95573	−	22.2271i	−0.302356	−	1.12841i
$389$	−6.17335			−0.313001			−0.156501	−	0.987678i	$-0.550021\pi$
$389$	−6.17335			−0.313001			−0.156501	+	0.987678i	$0.550021\pi$
$390$		0			0
$391$	−15.9914			−0.808722
$392$	−1.99745	−	7.45460i	−0.100887	−	0.376514i
$393$	28.0889	−	15.5704i	1.41690	−	0.785423i
$394$	−0.697088	+	0.402464i	−0.0351188	+	0.0202758i
$395$	2.70311	−	2.70311i	0.136008	−	0.136008i
$396$	−2.37417	−	10.2824i	−0.119306	−	0.516710i
$397$	23.0477	+	6.17560i	1.15673	+	0.309945i	0.785659	−	0.618660i	$-0.212324\pi$
$397$	23.0477	+	6.17560i	1.15673	+	0.309945i	0.371071	+	0.928605i	$0.378991\pi$
$398$	−4.57140	−	4.57140i	−0.229143	−	0.229143i
$399$	−9.91463	−	0.172930i	−0.496352	−	0.00865730i
$400$	−20.0382	−	11.5691i	−1.00191	−	0.578453i
$401$	22.4109	−	6.00499i	1.11915	−	0.299875i	0.348610	−	0.937268i	$-0.386654\pi$
$401$	22.4109	−	6.00499i	1.11915	−	0.299875i	0.770539	+	0.637393i	$0.219987\pi$
$402$	2.13901	−	3.56002i	0.106684	−	0.177558i
$403$		0			0
$404$		−	20.8129i		−	1.03548i
$405$	−29.5716	−	10.1806i	−1.46942	−	0.505877i
$406$	−0.550228	+	0.953023i	−0.0273074	+	0.0472978i
$407$	−2.02598	−	3.50910i	−0.100424	−	0.173940i
$408$	−13.5484	+	3.37818i	−0.670746	+	0.167245i
$409$	3.25292	−	12.1401i	0.160847	−	0.600288i	−0.837687	−	0.546151i	$-0.816093\pi$
$409$	3.25292	−	12.1401i	0.160847	−	0.600288i	0.998534	−	0.0541371i	$-0.0172408\pi$
$410$	−2.15750	+	8.05189i	−0.106551	+	0.397655i
$411$	−12.6630	+	3.15743i	−0.624622	+	0.155744i
$412$	4.15753	+	7.20106i	0.204827	+	0.354771i
$413$	5.81450	−	10.0710i	0.286113	−	0.495562i
$414$	2.09528	−	1.95398i	0.102977	−	0.0960329i
$415$			22.5532i			1.10709i
$416$		0			0
$417$	−4.81024	+	8.00582i	−0.235558	+	0.392047i
$418$	−3.14544	+	0.842818i	−0.153848	+	0.0412236i
$419$	−23.2172	−	13.4045i	−1.13424	−	0.654851i	−0.189239	−	0.981931i	$-0.560602\pi$
$419$	−23.2172	−	13.4045i	−1.13424	−	0.654851i	−0.944997	+	0.327080i	$0.893935\pi$
$420$	−13.1170	−	0.228786i	−0.640046	−	0.0111636i
$421$	−8.93430	−	8.93430i	−0.435431	−	0.435431i	0.455040	−	0.890471i	$-0.349625\pi$
$421$	−8.93430	−	8.93430i	−0.435431	−	0.435431i	−0.890471	+	0.455040i	$0.849625\pi$
$422$	2.72594	+	0.730414i	0.132697	+	0.0355560i
$423$	9.22649	−	2.13036i	0.448607	−	0.103582i
$424$	−2.37744	+	2.37744i	−0.115459	+	0.115459i
$425$	36.1633	−	20.8789i	1.75418	−	1.01278i
$426$	6.19716	−	3.43525i	0.300253	−	0.166438i
$427$	−0.800795	−	2.98861i	−0.0387532	−	0.144629i
$428$	−24.4891			−1.18372
$429$		0			0
$430$	6.79881			0.327868
$431$	−5.49370	−	20.5028i	−0.264622	−	0.987583i	−0.962481	−	0.271348i	$-0.912531\pi$
$431$	−5.49370	−	20.5028i	−0.264622	−	0.987583i	0.697859	−	0.716235i	$-0.254136\pi$
$432$	−9.25399	+	14.2511i	−0.445233	+	0.685658i
$433$	−1.60537	+	0.926859i	−0.0771490	+	0.0445420i	−0.538078	−	0.842895i	$-0.680850\pi$
$433$	−1.60537	+	0.926859i	−0.0771490	+	0.0445420i	0.460929	+	0.887437i	$0.347516\pi$
$434$	−1.32076	+	1.32076i	−0.0633986	+	0.0633986i
$435$	−11.2349	−	11.6338i	−0.538673	−	0.557798i
$436$	11.5007	+	3.08159i	0.550782	+	0.147582i
$437$	9.44007	+	9.44007i	0.451580	+	0.451580i
$438$	0.137496	−	7.88308i	0.00656979	−	0.376668i
$439$	12.4753	+	7.20264i	0.595415	+	0.343763i	0.767236	−	0.641365i	$-0.221632\pi$
$439$	12.4753	+	7.20264i	0.595415	+	0.343763i	−0.171820	+	0.985128i	$0.554965\pi$
$440$	−8.59840	+	2.30393i	−0.409913	+	0.109836i
$441$	14.9651	−	7.95761i	0.712625	−	0.378934i
$442$		0			0
$443$		−	22.2330i		−	1.05632i	−0.849144	−	0.528162i	$-0.822881\pi$
$443$		−	22.2330i		−	1.05632i	0.849144	−	0.528162i	$-0.177119\pi$
$444$	−1.93489	+	6.74811i	−0.0918260	+	0.320251i
$445$	−7.42603	+	12.8623i	−0.352027	+	0.609729i
$446$	4.98965	+	8.64232i	0.236267	+	0.409226i
$447$	9.55963	+	38.3394i	0.452155	+	1.81339i
$448$	−1.55521	+	5.80413i	−0.0734769	+	0.274220i
$449$	−6.36268	+	23.7458i	−0.300273	+	1.12064i	0.636665	+	0.771141i	$0.280313\pi$
$449$	−6.36268	+	23.7458i	−0.300273	+	1.12064i	−0.936938	+	0.349495i	$0.886353\pi$
$450$	−2.18712	+	7.15442i	−0.103102	+	0.337263i
$451$	−6.38188	−	11.0537i	−0.300511	−	0.520501i
$452$	12.2044	−	21.1387i	0.574048	−	0.994281i
$453$	15.5845	+	4.46857i	0.732225	+	0.209952i
$454$		−	2.59229i		−	0.121662i
$455$		0			0
$456$	9.99211	+	6.00368i	0.467923	+	0.281148i
$457$	6.53825	−	1.75192i	0.305847	−	0.0819513i	−0.102632	−	0.994719i	$-0.532726\pi$
$457$	6.53825	−	1.75192i	0.305847	−	0.0819513i	0.408478	+	0.912768i	$0.366060\pi$
$458$	4.92490	+	2.84339i	0.230125	+	0.132863i
$459$	−13.9231	−	27.3230i	−0.649876	−	1.27533i
$460$	12.4892	+	12.4892i	0.582312	+	0.582312i
$461$	11.9685	+	3.20695i	0.557429	+	0.149363i	0.526525	−	0.850160i	$-0.323495\pi$
$461$	11.9685	+	3.20695i	0.557429	+	0.149363i	0.0309044	+	0.999522i	$0.490161\pi$
$462$	−0.956871	+	0.924064i	−0.0445177	+	0.0429914i
$463$	6.97385	−	6.97385i	0.324102	−	0.324102i	−0.526236	−	0.850339i	$-0.676397\pi$
$463$	6.97385	−	6.97385i	0.324102	−	0.324102i	0.850339	+	0.526236i	$0.176397\pi$
$464$	−7.60980	+	4.39352i	−0.353276	+	0.203964i
$465$	−13.3089	−	24.0091i	−0.617184	−	1.11339i
$466$	1.65612	+	6.18074i	0.0767185	+	0.286317i
$467$	−9.19934			−0.425695			−0.212847	−	0.977085i	$-0.568274\pi$
$467$	−9.19934			−0.425695			−0.212847	+	0.977085i	$0.568274\pi$
$468$		0			0
$469$	7.90563			0.365048
$470$	−1.00054	−	3.73407i	−0.0461515	−	0.172240i
$471$	13.1658	+	23.7510i	0.606647	+	1.09439i
$472$	−11.8391	+	6.83530i	−0.544938	+	0.314620i
$473$	−7.36110	+	7.36110i	−0.338464	+	0.338464i
$474$	−0.483064	+	0.466501i	−0.0221878	+	0.0214271i
$475$	−33.6732	−	9.02270i	−1.54503	−	0.413990i
$476$	−9.09592	−	9.09592i	−0.416911	−	0.416911i
$477$	−6.26215	−	3.91280i	−0.286724	−	0.179155i
$478$	2.82415	+	1.63052i	0.129174	+	0.0745784i
$479$	−22.1676	+	5.93980i	−1.01287	+	0.271396i	−0.726826	−	0.686821i	$-0.759005\pi$
$479$	−22.1676	+	5.93980i	−1.01287	+	0.271396i	−0.286039	+	0.958218i	$0.592339\pi$
$480$	20.0412	+	12.0416i	0.914750	+	0.549621i
$481$		0			0
$482$		−	9.75464i		−	0.444312i
$483$	5.24229	+	1.50313i	0.238533	+	0.0683947i
$484$	−7.01850	+	12.1564i	−0.319023	+	0.552563i
$485$	−21.3148	−	36.9183i	−0.967854	−	1.67637i
$486$	5.16285	+	1.87874i	0.234192	+	0.0852213i
$487$	−7.62733	+	28.4656i	−0.345627	+	1.28990i	0.546250	+	0.837622i	$0.316055\pi$
$487$	−7.62733	+	28.4656i	−0.345627	+	1.28990i	−0.891878	+	0.452277i	$0.850612\pi$
$488$	−0.941384	+	3.51329i	−0.0426144	+	0.159039i
$489$	−1.44838	−	5.80879i	−0.0654978	−	0.262682i
$490$	−3.45975	−	5.99247i	−0.156296	−	0.270712i
$491$	7.66195	−	13.2709i	0.345779	−	0.598907i	−0.639716	−	0.768611i	$-0.720948\pi$
$491$	7.66195	−	13.2709i	0.345779	−	0.598907i	0.985495	+	0.169705i	$0.0542814\pi$
$492$	−6.09496	+	21.2567i	−0.274782	+	0.958326i
$493$		−	15.8582i		−	0.714215i
$494$		0			0
$495$	−9.17859	−	17.2613i	−0.412547	−	0.775838i
$496$	−14.4063	+	3.86016i	−0.646863	+	0.173326i
$497$	11.6805	+	6.74372i	0.523941	+	0.302497i
$498$	0.0690926	−	3.96131i	0.00309611	−	0.177510i
$499$	29.5332	+	29.5332i	1.32209	+	1.32209i	0.912084	+	0.410004i	$0.134473\pi$
$499$	29.5332	+	29.5332i	1.32209	+	1.32209i	0.410004	+	0.912084i	$0.365527\pi$
$500$	−13.0684	−	3.50168i	−0.584439	−	0.156600i
$501$	6.30871	+	6.53269i	0.281852	+	0.291859i
$502$	−1.39562	+	1.39562i	−0.0622897	+	0.0622897i
$503$	30.1073	−	17.3825i	1.34242	−	0.775046i	0.355257	−	0.934768i	$-0.384393\pi$
$503$	30.1073	−	17.3825i	1.34242	−	0.775046i	0.987162	+	0.159722i	$0.0510599\pi$
$504$	4.75895	+	0.166060i	0.211981	+	0.00739692i
$505$	−9.97931	−	37.2433i	−0.444073	−	1.65730i
$506$	1.79091			0.0796155
$507$		0			0
$508$	−14.6199			−0.648653
$509$	−11.4648	−	42.7871i	−0.508167	−	1.89651i	−0.438011	−	0.898969i	$-0.644317\pi$
$509$	−11.4648	−	42.7871i	−0.508167	−	1.89651i	−0.0701558	−	0.997536i	$-0.522350\pi$
$510$	−10.9495	+	6.06962i	−0.484854	+	0.268767i
$511$	12.9971	−	7.50387i	0.574957	−	0.331952i
$512$	15.2996	−	15.2996i	0.676153	−	0.676153i
$513$	−7.91022	+	24.3484i	−0.349245	+	1.07501i
$514$	2.31958	+	0.621529i	0.102312	+	0.0274145i
$515$	10.8924	+	10.8924i	0.479975	+	0.479975i
$516$	18.0329	+	0.314527i	0.793854	+	0.0138463i
$517$	5.12618	+	2.95960i	0.225449	+	0.130163i
$518$	0.854741	−	0.229027i	0.0375552	−	0.0100629i
$519$	−12.7128	+	21.1584i	−0.558032	+	0.928749i
$520$		0			0
$521$		−	1.93372i		−	0.0847179i	−0.999102	−	0.0423590i	$-0.986513\pi$
$521$		−	1.93372i		−	0.0847179i	0.999102	−	0.0423590i	$-0.0134873\pi$
$522$	1.93769	+	2.07781i	0.0848106	+	0.0909434i
$523$	−0.753051	+	1.30432i	−0.0329286	+	0.0570340i	−0.882020	−	0.471212i	$-0.843817\pi$
$523$	−0.753051	+	1.30432i	−0.0329286	+	0.0570340i	0.849091	+	0.528246i	$0.177150\pi$
$524$	−17.3904	−	30.1211i	−0.759705	−	1.31585i
$525$	−13.8175	+	3.44529i	−0.603047	+	0.150365i
$526$	−2.06445	+	7.70463i	−0.0900142	+	0.335938i
$527$	6.96651	−	25.9994i	0.303466	−	1.13255i
$528$	−10.3062	+	2.56976i	−0.448519	+	0.111835i
$529$	7.82890	+	13.5601i	0.340387	+	0.589568i
$530$	−1.50726	+	2.61066i	−0.0654714	+	0.113400i
$531$	−20.4764	−	21.9571i	−0.888602	−	0.952859i
$532$			10.7390i			0.465595i
$533$		0			0
$534$	1.34373	−	2.23641i	0.0581490	−	0.0967791i
$535$	−43.8215	+	11.7419i	−1.89457	+	0.507648i
$536$	−8.04846	−	4.64678i	−0.347640	−	0.200710i
$537$	−7.56215	−	0.131898i	−0.326331	−	0.00569182i
$538$	−6.50526	−	6.50526i	−0.280462	−	0.280462i
$539$	10.2340	+	2.74218i	0.440808	+	0.118114i
$540$	−10.4652	+	32.2130i	−0.450351	+	1.38623i
$541$	−2.56375	+	2.56375i	−0.110224	+	0.110224i	−0.760068	−	0.649844i	$-0.774834\pi$
$541$	−2.56375	+	2.56375i	−0.110224	+	0.110224i	0.649844	+	0.760068i	$0.274834\pi$
$542$	−5.39710	+	3.11602i	−0.231825	+	0.133844i
$543$	3.19242	−	1.76964i	0.137000	−	0.0759425i
$544$	5.93348	+	22.1441i	0.254396	+	0.949419i
$545$	22.0572			0.944827
$546$		0			0
$547$	23.1549			0.990030			0.495015	−	0.868884i	$-0.335163\pi$
$547$	23.1549			0.990030			0.495015	+	0.868884i	$0.335163\pi$
$548$	3.65808	+	13.6522i	0.156266	+	0.583191i
$549$	−7.98321	−	0.278569i	−0.340715	−	0.0118890i
$550$	−4.04999	+	2.33826i	−0.172692	+	0.0997038i
$551$	−9.36139	+	9.36139i	−0.398809	+	0.398809i
$552$	−4.45349	−	4.61161i	−0.189553	−	0.196283i
$553$	−1.23473	−	0.330846i	−0.0525062	−	0.0140690i
$554$	5.65736	+	5.65736i	0.240358	+	0.240358i
$555$	−0.226797	+	13.0030i	−0.00962700	+	0.551948i
$556$	8.75970	+	5.05741i	0.371494	+	0.214482i
$557$	3.45636	−	0.926129i	0.146451	−	0.0392414i	−0.184849	−	0.982767i	$-0.559180\pi$
$557$	3.45636	−	0.926129i	0.146451	−	0.0392414i	0.331300	+	0.943526i	$0.392513\pi$
$558$	2.26406	+	4.25780i	0.0958451	+	0.180247i
$559$		0			0
$560$			13.2045i			0.557994i
$561$	5.28351	−	18.4267i	0.223070	−	0.777977i
$562$	2.13267	−	3.69389i	0.0899611	−	0.155817i
$563$	9.83710	+	17.0384i	0.414585	+	0.718081i	0.995385	−	0.0959647i	$-0.0305936\pi$
$563$	9.83710	+	17.0384i	0.414585	+	0.718081i	−0.580800	+	0.814046i	$0.697260\pi$
$564$	−2.48105	−	9.95039i	−0.104471	−	0.418987i
$565$	11.7035	−	43.6781i	0.492370	−	1.83755i
$566$	−0.648166	+	2.41899i	−0.0272445	+	0.101678i
$567$	1.99601	+	10.2657i	0.0838247	+	0.431119i
$568$	−7.92766	−	13.7311i	−0.332637	−	0.576145i
$569$	−4.78231	+	8.28321i	−0.200485	+	0.347250i	−0.948685	−	0.316223i	$-0.897585\pi$
$569$	−4.78231	+	8.28321i	−0.200485	+	0.347250i	0.748200	+	0.663473i	$0.230918\pi$
$570$	10.0468	+	2.88072i	0.420813	+	0.120660i
$571$		−	17.9785i		−	0.752375i	−0.926544	−	0.376187i	$-0.877235\pi$
$571$		−	17.9785i		−	0.752375i	0.926544	−	0.376187i	$-0.122765\pi$
$572$		0			0
$573$	−10.0925	−	6.06399i	−0.421619	−	0.253327i
$574$	2.69245	−	0.721441i	0.112381	−	0.0301124i
$575$	16.6038	+	9.58619i	0.692425	+	0.399772i
$576$	13.1564	+	8.22057i	0.548185	+	0.342524i
$577$	−6.37509	−	6.37509i	−0.265398	−	0.265398i	0.561844	−	0.827243i	$-0.310092\pi$
$577$	−6.37509	−	6.37509i	−0.265398	−	0.265398i	−0.827243	+	0.561844i	$0.810092\pi$
$578$	−6.06984	−	1.62641i	−0.252472	−	0.0676497i
$579$	13.8499	−	13.3750i	0.575582	−	0.555848i
$580$	−12.3851	+	12.3851i	−0.514264	+	0.514264i
$581$	6.53113	−	3.77075i	0.270957	−	0.156437i
$582$	3.63069	+	6.54973i	0.150497	+	0.271495i
$583$	−1.19465	−	4.45849i	−0.0494773	−	0.184652i
$584$	−17.6425			−0.730053
$585$		0			0
$586$	5.60209			0.231420
$587$	8.12231	+	30.3129i	0.335243	+	1.25115i	0.903605	+	0.428367i	$0.140911\pi$
$587$	8.12231	+	30.3129i	0.335243	+	1.25115i	−0.568362	+	0.822779i	$0.692423\pi$
$588$	−8.89929	−	16.0542i	−0.367000	−	0.662066i
$589$	−19.4604	+	11.2355i	−0.801853	+	0.462950i
$590$	−8.66697	+	8.66697i	−0.356814	+	0.356814i
$591$	−2.84548	+	2.74792i	−0.117047	+	0.113034i
$592$	6.82503	+	1.82876i	0.280507	+	0.0751616i
$593$	−23.7211	−	23.7211i	−0.974108	−	0.974108i	0.0255650	−	0.999673i	$-0.491862\pi$
$593$	−23.7211	−	23.7211i	−0.974108	−	0.974108i	−0.999673	+	0.0255650i	$0.991862\pi$
$594$	1.55927	+	3.05995i	0.0639778	+	0.125551i
$595$	−20.6378	−	11.9153i	−0.846069	−	0.488478i
$596$	41.3341	−	11.0754i	1.69311	−	0.453668i
$597$	−27.2335	−	16.3630i	−1.11459	−	0.669695i
$598$		0			0
$599$			33.7915i			1.38068i	0.723484	+	0.690341i	$0.242540\pi$
$599$			33.7915i			1.38068i	−0.723484	+	0.690341i	$0.757460\pi$
$600$	16.0923	+	4.61415i	0.656964	+	0.188372i
$601$	15.0742	−	26.1092i	0.614888	−	1.06502i	−0.375516	−	0.926816i	$-0.622534\pi$
$601$	15.0742	−	26.1092i	0.614888	−	1.06502i	0.990404	−	0.138202i	$-0.0441323\pi$
$602$	−1.13672	−	1.96886i	−0.0463292	−	0.0802446i
$603$	5.96693	−	19.5188i	0.242992	−	0.794867i
$604$	4.54432	−	16.9596i	0.184906	−	0.690077i
$605$	−6.73042	+	25.1183i	−0.273630	+	1.02120i
$606$	1.63870	+	6.57209i	0.0665676	+	0.266973i
$607$	−11.0198	−	19.0869i	−0.447281	−	0.774713i	0.550927	−	0.834553i	$-0.314274\pi$
$607$	−11.0198	−	19.0869i	−0.447281	−	0.774713i	−0.998208	+	0.0598403i	$0.980941\pi$
$608$	9.56943	−	16.5747i	0.388092	−	0.672195i
$609$	−1.49060	+	5.19860i	−0.0604022	+	0.210658i
$610$			3.26111i			0.132038i
$611$		0			0
$612$	−29.3229	+	15.5923i	−1.18531	+	0.630280i
$613$	−0.571244	+	0.153064i	−0.0230723	+	0.00618221i	−0.270337	−	0.962766i	$-0.587135\pi$
$613$	−0.571244	+	0.153064i	−0.0230723	+	0.00618221i	0.247264	+	0.968948i	$0.420468\pi$
$614$	6.20916	+	3.58486i	0.250581	+	0.144673i
$615$	−0.714416	+	40.9599i	−0.0288080	+	1.65166i
$616$	2.10479	+	2.10479i	0.0848044	+	0.0848044i
$617$	−28.0800	−	7.52400i	−1.13046	−	0.302905i	−0.355349	−	0.934734i	$-0.615638\pi$
$617$	−28.0800	−	7.52400i	−1.13046	−	0.302905i	−0.775108	+	0.631829i	$0.782305\pi$
$618$	−1.87980	−	1.94654i	−0.0756166	−	0.0783012i
$619$	22.7868	−	22.7868i	0.915881	−	0.915881i	−0.0808459	−	0.996727i	$-0.525762\pi$
$619$	22.7868	−	22.7868i	0.915881	−	0.915881i	0.996727	+	0.0808459i	$0.0257622\pi$
$620$	−25.7461	+	14.8645i	−1.03399	+	0.596974i
$621$	7.66791	−	11.8086i	0.307703	−	0.473862i
$622$	−0.695256	−	2.59473i	−0.0278772	−	0.104039i
$623$	4.96634			0.198972
$624$		0			0
$625$	10.3139			0.412556
$626$	−0.594282	−	2.21789i	−0.0237523	−	0.0886448i
$627$	−13.9966	+	7.75870i	−0.558972	+	0.309853i
$628$	25.4694	−	14.7047i	1.01634	−	0.586783i
$629$	−9.01686	+	9.01686i	−0.359526	+	0.359526i
$630$	4.15999	−	0.960524i	0.165738	−	0.0382682i
$631$	39.1937	+	10.5019i	1.56028	+	0.418075i	0.932751	−	0.360521i	$-0.117401\pi$
$631$	39.1937	+	10.5019i	1.56028	+	0.418075i	0.627526	+	0.778596i	$0.284068\pi$
$632$	1.06258	+	1.06258i	0.0422670	+	0.0422670i
$633$	13.8668	+	0.241863i	0.551157	+	0.00961320i
$634$	−2.71690	−	1.56860i	−0.107902	−	0.0622971i
$635$	−26.1613	+	7.00990i	−1.03818	+	0.278180i
$636$	−4.11858	+	6.85468i	−0.163312	+	0.271806i
$637$		0			0
$638$			1.77598i			0.0703117i
$639$	25.4662	−	23.7488i	1.00743	−	0.939489i
$640$	16.6654	−	28.8653i	0.658758	−	1.14100i
$641$	12.8560	+	22.2673i	0.507783	+	0.879506i	0.999959	+	0.00901077i	$0.00286825\pi$
$641$	12.8560	+	22.2673i	0.507783	+	0.879506i	−0.492176	+	0.870496i	$0.663798\pi$
$642$	7.73291	−	1.92814i	0.305194	−	0.0760976i
$643$	−0.164018	+	0.612124i	−0.00646824	+	0.0241398i	−0.969085	−	0.246729i	$-0.920644\pi$
$643$	−0.164018	+	0.612124i	−0.00646824	+	0.0241398i	0.962616	+	0.270869i	$0.0873109\pi$
$644$	1.52861	−	5.70484i	0.0602356	−	0.224802i
$645$	32.4195	−	8.08354i	1.27652	−	0.318289i
$646$	5.12404	+	8.87510i	0.201603	+	0.349186i
$647$	−23.5124	+	40.7247i	−0.924368	+	1.60105i	−0.131794	+	0.991277i	$0.542074\pi$
$647$	−23.5124	+	40.7247i	−0.924368	+	1.60105i	−0.792574	+	0.609776i	$0.791260\pi$
$648$	4.00191	−	11.6244i	0.157210	−	0.456649i
$649$		−	18.7675i		−	0.736690i
$650$		0			0
$651$	−4.72758	+	7.86826i	−0.185289	+	0.308381i
$652$	−6.26251	+	1.67804i	−0.245259	+	0.0657169i
$653$	−25.0935	−	14.4877i	−0.981984	−	0.566949i	−0.0791154	−	0.996865i	$-0.525210\pi$
$653$	−25.0935	−	14.4877i	−0.981984	−	0.566949i	−0.902869	+	0.429917i	$0.858543\pi$
$654$	−3.87419	−	0.0675732i	−0.151493	−	0.00264232i
$655$	−45.5614	−	45.5614i	−1.78023	−	1.78023i
$656$	21.4990	+	5.76064i	0.839394	+	0.224915i
$657$	−8.71705	−	37.7532i	−0.340085	−	1.47289i
$658$	−0.914059	+	0.914059i	−0.0356337	+	0.0356337i
$659$	−40.4280	+	23.3411i	−1.57485	+	0.909241i	−0.579290	+	0.815121i	$0.696670\pi$
$659$	−40.4280	+	23.3411i	−1.57485	+	0.909241i	−0.995561	+	0.0941194i	$0.969996\pi$
$660$	−18.5175	+	10.2648i	−0.720794	+	0.399555i
$661$	−1.79701	−	6.70655i	−0.0698957	−	0.260854i	0.922132	−	0.386876i	$-0.126446\pi$
$661$	−1.79701	−	6.70655i	−0.0698957	−	0.260854i	−0.992028	+	0.126021i	$0.959779\pi$
$662$	−5.66611			−0.220220
$663$		0			0
$664$	−8.86551			−0.344048
$665$	5.14911	+	19.2167i	0.199674	+	0.745194i
$666$	0.0796706	−	2.28320i	0.00308717	−	0.0884721i
$667$	6.30553	−	3.64050i	0.244151	−	0.140961i
$668$	6.95457	−	6.95457i	0.269080	−	0.269080i
$669$	34.0680	+	35.2776i	1.31715	+	1.36391i
$670$	−8.04861	−	2.15662i	−0.310945	−	0.0833174i
$671$	−3.53081	−	3.53081i	−0.136306	−	0.136306i
$672$	0.136342	−	7.81696i	0.00525952	−	0.301546i
$673$	22.6855	+	13.0975i	0.874460	+	0.504870i	0.868828	−	0.495114i	$-0.164874\pi$
$673$	22.6855	+	13.0975i	0.874460	+	0.504870i	0.00563228	+	0.999984i	$0.498207\pi$
$674$	−9.65322	+	2.58657i	−0.371828	+	0.0996311i
$675$	−1.92272	+	36.7156i	−0.0740057	+	1.41318i
$676$		0			0
$677$		−	21.9298i		−	0.842829i	−0.906868	−	0.421415i	$-0.861534\pi$
$677$		−	21.9298i		−	0.842829i	0.906868	−	0.421415i	$-0.138466\pi$
$678$	−2.18945	+	7.63589i	−0.0840852	+	0.293255i
$679$	−7.12739	+	12.3450i	−0.273524	+	0.473758i
$680$	14.0071	+	24.2610i	0.537149	+	0.930369i
$681$	−3.08213	−	12.3611i	−0.118108	−	0.473677i
$682$	−0.780190	+	2.91171i	−0.0298750	+	0.111495i
$683$	−1.97300	+	7.36335i	−0.0754949	+	0.281751i	−0.993345	−	0.115176i	$-0.963257\pi$
$683$	−1.97300	+	7.36335i	−0.0754949	+	0.281751i	0.917850	+	0.396927i	$0.129923\pi$
$684$	26.5144	+	8.10549i	1.01380	+	0.309921i
$685$	13.0918	+	22.6757i	0.500212	+	0.866392i
$686$	−2.59028	+	4.48650i	−0.0988975	+	0.171296i
$687$	26.8646	+	7.70291i	1.02495	+	0.293884i
$688$		−	18.1532i		−	0.692084i
$689$		0			0
$690$	−4.92706	−	2.96039i	−0.187570	−	0.112700i
$691$	15.4088	−	4.12878i	0.586179	−	0.157066i	0.0464729	−	0.998920i	$-0.485202\pi$
$691$	15.4088	−	4.12878i	0.586179	−	0.157066i	0.539707	+	0.841853i	$0.318535\pi$
$692$	23.1508	+	13.3661i	0.880061	+	0.508103i
$693$	−3.46407	+	5.54399i	−0.131589	+	0.210599i
$694$	−2.75978	−	2.75978i	−0.104760	−	0.104760i
$695$	18.0998	+	4.84983i	0.686565	+	0.183965i
$696$	4.57317	−	4.41637i	0.173345	−	0.167402i
$697$	−28.4033	+	28.4033i	−1.07585	+	1.07585i
$698$	−9.13155	+	5.27210i	−0.345634	+	0.199552i
$699$	15.2457	+	27.5032i	0.576647	+	1.04027i
$700$	3.99159	+	14.8968i	0.150868	+	0.563047i
$701$	30.3059			1.14464			0.572319	−	0.820031i	$-0.306044\pi$
$701$	30.3059			1.14464			0.572319	+	0.820031i	$0.306044\pi$
$702$		0			0
$703$	10.6457			0.401509
$704$	2.50989	+	9.36704i	0.0945951	+	0.353034i
$705$	−9.21066	−	16.6160i	−0.346893	−	0.625793i
$706$	3.86907	−	2.23381i	0.145615	−	0.0840706i
$707$	−9.11674	+	9.11674i	−0.342870	+	0.342870i
$708$	−23.3889	+	22.5870i	−0.879008	+	0.848871i
$709$	−32.8514	−	8.80249i	−1.23376	−	0.330585i	−0.417717	−	0.908577i	$-0.637170\pi$
$709$	−32.8514	−	8.80249i	−1.23376	−	0.330585i	−0.816042	+	0.577993i	$0.803836\pi$
$710$	−10.0521	−	10.0521i	−0.377247	−	0.377247i
$711$	−1.74879	+	2.79881i	−0.0655847	+	0.104964i
$712$	−5.05607	−	2.91912i	−0.189484	−	0.109399i
$713$	11.9372	−	3.19855i	0.447050	−	0.119787i
$714$	3.58839	+	2.15606i	0.134292	+	0.0806884i
$715$		0			0
$716$			8.19093i			0.306110i
$717$	15.4053	+	4.41718i	0.575322	+	0.164963i
$718$	−5.08050	+	8.79968i	−0.189602	+	0.328401i
$719$	−3.94839	−	6.83882i	−0.147250	−	0.255045i	0.782960	−	0.622072i	$-0.213709\pi$
$719$	−3.94839	−	6.83882i	−0.147250	−	0.255045i	−0.930210	+	0.367027i	$0.880376\pi$
$720$	32.6017	+	9.96640i	1.21499	+	0.371426i
$721$	1.33316	−	4.97544i	0.0496496	−	0.185295i
$722$	0.481159	−	1.79571i	0.0179069	−	0.0668294i
$723$	−11.5979	−	46.5140i	−0.431331	−	1.72988i
$724$	−1.97649	−	3.42339i	−0.0734558	−	0.127229i
$725$	−9.50629	+	16.4654i	−0.353055	+	0.611509i
$726$	1.25910	−	4.39123i	0.0467296	−	0.162974i
$727$		−	24.6824i		−	0.915420i	−0.889102	−	0.457710i	$-0.848670\pi$
$727$		−	24.6824i		−	0.915420i	0.889102	−	0.457710i	$-0.151330\pi$
$728$		0			0
$729$	26.8523	+	2.82014i	0.994530	+	0.104450i
$730$	−15.2792	+	4.09404i	−0.565507	+	0.151527i
$731$	28.3722	+	16.3807i	1.04939	+	0.605863i
$732$	−0.150866	+	8.64963i	−0.00557616	+	0.319700i
$733$	34.3405	+	34.3405i	1.26839	+	1.26839i	0.946918	+	0.321476i	$0.104179\pi$
$733$	34.3405	+	34.3405i	1.26839	+	1.26839i	0.321476	+	0.946918i	$0.395821\pi$
$734$	7.87731	+	2.11072i	0.290757	+	0.0779081i
$735$	−23.6223	−	24.4610i	−0.871323	−	0.902257i
$736$	−7.44281	+	7.44281i	−0.274346	+	0.274346i
$737$	11.0492	−	6.37928i	0.407004	−	0.234984i
$738$	0.250964	−	7.19212i	0.00923812	−	0.264746i
$739$	10.0551	+	37.5261i	0.369882	+	1.38042i	0.860680	+	0.509146i	$0.170039\pi$
$739$	10.0551	+	37.5261i	0.369882	+	1.38042i	−0.490798	+	0.871273i	$0.663295\pi$
$740$	14.0842			0.517746
$741$		0			0
$742$	1.00802			0.0370056
$743$	13.4913	+	50.3503i	0.494949	+	1.84717i	0.530316	+	0.847800i	$0.322073\pi$
$743$	13.4913	+	50.3503i	0.494949	+	1.84717i	−0.0353674	+	0.999374i	$0.511260\pi$
$744$	9.43781	−	5.23162i	0.346007	−	0.191801i
$745$	68.6542	−	39.6375i	2.51530	−	1.45221i
$746$	5.10435	−	5.10435i	0.186883	−	0.186883i
$747$	−4.38039	−	18.9713i	−0.160270	−	0.694122i
$748$	−20.0526	−	5.37308i	−0.733195	−	0.196459i
$749$	10.7270	+	10.7270i	0.391957	+	0.391957i
$750$	4.40233	+	0.0767848i	0.160750	+	0.00280378i
$751$	−42.7471	−	24.6801i	−1.55986	−	0.900588i	−0.997269	−	0.0738552i	$-0.976470\pi$
$751$	−42.7471	−	24.6801i	−1.55986	−	0.900588i	−0.562595	−	0.826733i	$-0.690197\pi$
$752$	−9.97017	+	2.67150i	−0.363575	+	0.0974196i
$753$	−4.99555	+	8.31423i	−0.182048	+	0.302987i
$754$		0			0
$755$		−	32.5270i		−	1.18378i
$756$	11.0782	−	2.35521i	0.402911	−	0.0856580i
$757$	−9.42818	+	16.3301i	−0.342673	+	0.593527i	−0.984928	−	0.172964i	$-0.944666\pi$
$757$	−9.42818	+	16.3301i	−0.342673	+	0.593527i	0.642255	+	0.766491i	$0.277999\pi$
$758$	−0.699838	−	1.21216i	−0.0254193	−	0.0440275i
$759$	8.53976	−	2.12932i	0.309974	−	0.0772895i
$760$	6.05310	−	22.5905i	0.219569	−	0.819443i
$761$	9.96144	−	37.1766i	0.361102	−	1.34765i	−0.511527	−	0.859267i	$-0.670920\pi$
$761$	9.96144	−	37.1766i	0.361102	−	1.34765i	0.872629	−	0.488384i	$-0.162413\pi$
$762$	4.61653	−	1.15109i	0.167239	−	0.0416997i
$763$	−3.68783	−	6.38751i	−0.133508	−	0.231243i
$764$	−6.37559	+	11.0428i	−0.230661	+	0.399516i
$765$	−44.9953	+	41.9610i	−1.62681	+	1.51710i
$766$		−	9.37896i		−	0.338876i
$767$		0			0
$768$	6.21032	−	10.3360i	0.224096	−	0.372969i
$769$	2.75634	−	0.738559i	0.0993962	−	0.0266331i	−0.208778	−	0.977963i	$-0.566949\pi$
$769$	2.75634	−	0.738559i	0.0993962	−	0.0266331i	0.308174	+	0.951330i	$0.400282\pi$
$770$	2.31126	+	1.33441i	0.0832921	+	0.0480887i
$771$	11.7997	+	0.205808i	0.424954	+	0.00741200i
$772$	−14.7443	−	14.7443i	−0.530660	−	0.530660i
$773$	6.20770	+	1.66335i	0.223275	+	0.0598265i	0.368722	−	0.929540i	$-0.379795\pi$
$773$	6.20770	+	1.66335i	0.223275	+	0.0598265i	−0.145447	+	0.989366i	$0.546462\pi$
$774$	−5.71902	+	1.32050i	−0.205566	+	0.0474643i
$775$	−22.8188	+	22.8188i	−0.819675	+	0.819675i
$776$	14.5123	−	8.37869i	0.520962	−	0.300777i
$777$	3.80344	−	2.10835i	0.136448	−	0.0756366i
$778$	−0.563129	−	2.10162i	−0.0201891	−	0.0753469i
$779$	33.5341			1.20148
$780$		0			0
$781$	21.7668			0.778878
$782$	−1.45873	−	5.44405i	−0.0521640	−	0.194679i
$783$	11.7102	+	7.60400i	0.418487	+	0.271745i
$784$	−16.0002	+	9.23773i	−0.571436	+	0.329919i
$785$	38.5251	−	38.5251i	1.37502	−	1.37502i
$786$	7.86296	+	8.14212i	0.280463	+	0.290420i
$787$	14.6513	+	3.92580i	0.522262	+	0.139940i	0.510313	−	0.859989i	$-0.329530\pi$
$787$	14.6513	+	3.92580i	0.522262	+	0.139940i	0.0119493	+	0.999929i	$0.496196\pi$
$788$	3.02924	+	3.02924i	0.107912	+	0.107912i
$789$	−0.683604	+	39.1933i	−0.0243370	+	1.39532i
$790$	1.16681	+	0.673658i	0.0415132	+	0.0239677i
$791$	−14.6054	+	3.91350i	−0.519308	+	0.139148i
$792$	6.78531	−	3.60804i	0.241105	−	0.128206i
$793$		0			0
$794$			8.40957i			0.298444i
$795$	−4.08327	+	14.2408i	−0.144819	+	0.505067i
$796$	−17.2039	+	29.7980i	−0.609775	+	1.05616i
$797$	0.789625	+	1.36767i	0.0279700	+	0.0484454i	0.879672	−	0.475582i	$-0.157762\pi$
$797$	0.789625	+	1.36767i	0.0279700	+	0.0484454i	−0.851702	+	0.524027i	$0.824429\pi$
$798$	−0.845534	−	3.39106i	−0.0299316	−	0.120042i
$799$	4.82131	−	17.9934i	0.170566	−	0.636560i
$800$	7.11374	−	26.5489i	0.251509	−	0.938644i
$801$	3.74845	−	12.2618i	0.132445	−	0.433248i
$802$	4.08862	+	7.08170i	0.144374	+	0.250063i
$803$	12.1102	−	20.9754i	0.427359	−	0.740207i
$804$	−21.2480	−	6.09247i	−0.749360	−	0.214865i
$805$		−	10.9414i		−	0.385633i
$806$		0			0
$807$	−38.7542	−	23.2852i	−1.36421	−	0.819677i
$808$	14.6401	−	3.92280i	0.515037	−	0.138004i
$809$	−10.5758	−	6.10595i	−0.371826	−	0.214674i	0.302430	−	0.953172i	$-0.402202\pi$
$809$	−10.5758	−	6.10595i	−0.371826	−	0.214674i	−0.674256	+	0.738498i	$0.735536\pi$
$810$	0.768323	−	10.9959i	0.0269961	−	0.386356i
$811$	−29.6037	−	29.6037i	−1.03952	−	1.03952i	−0.999186	−	0.0403387i	$-0.987156\pi$
$811$	−29.6037	−	29.6037i	−1.03952	−	1.03952i	−0.0403387	−	0.999186i	$-0.512844\pi$
$812$	5.65729	+	1.51587i	0.198532	+	0.0531965i
$813$	−22.0307	+	21.2754i	−0.772651	+	0.746160i
$814$	1.00981	−	1.00981i	0.0353939	−	0.0353939i
$815$	−10.4018	+	6.00546i	−0.364358	+	0.210362i
$816$	16.2062	+	29.2359i	0.567331	+	1.02346i
$817$	−7.07884	−	26.4186i	−0.247657	−	0.924269i
$818$	4.42964			0.154879
$819$		0			0
$820$	44.3656			1.54931
$821$	−4.81637	−	17.9749i	−0.168093	−	0.627330i	−0.997625	−	0.0688721i	$-0.978060\pi$
$821$	−4.81637	−	17.9749i	−0.168093	−	0.627330i	0.829533	−	0.558458i	$-0.188607\pi$
$822$	−2.23001	−	4.02293i	−0.0777807	−	0.140316i
$823$	−0.447230	+	0.258209i	−0.0155895	+	0.00900059i	−0.507774	−	0.861490i	$-0.669532\pi$
$823$	−0.447230	+	0.258209i	−0.0155895	+	0.00900059i	0.492185	+	0.870491i	$0.336198\pi$
$824$	−4.28172	+	4.28172i	−0.149161	+	0.149161i
$825$	−16.5319	+	15.9651i	−0.575566	+	0.555832i
$826$	3.95892	+	1.06079i	0.137748	+	0.0369096i
$827$	21.0701	+	21.0701i	0.732678	+	0.732678i	0.971149	−	0.238472i	$-0.0766464\pi$
$827$	21.0701	+	21.0701i	0.732678	+	0.732678i	−0.238472	+	0.971149i	$0.576646\pi$
$828$	−12.9314	−	8.07994i	−0.449396	−	0.280797i
$829$	1.46119	+	0.843616i	0.0507491	+	0.0293000i	0.525160	−	0.851004i	$-0.324006\pi$
$829$	1.46119	+	0.843616i	0.0507491	+	0.0293000i	−0.474411	+	0.880304i	$0.657339\pi$
$830$	−7.67790	+	2.05729i	−0.266504	+	0.0714094i
$831$	33.7030	+	20.2502i	1.16914	+	0.702471i
$832$		0			0
$833$		−	33.3430i		−	1.15527i
$834$	−3.16425	−	0.907288i	−0.109569	−	0.0314168i
$835$	9.11018	−	15.7793i	0.315271	−	0.546065i
$836$	8.66562	+	15.0093i	0.299707	+	0.519107i
$837$	15.8583	+	17.6110i	0.548143	+	0.608726i
$838$	2.44549	−	9.12670i	0.0844781	−	0.315277i
$839$	2.80444	−	10.4663i	0.0968199	−	0.361337i	−0.900469	−	0.434920i	$-0.856777\pi$
$839$	2.80444	−	10.4663i	0.0968199	−	0.361337i	0.997289	+	0.0735829i	$0.0234434\pi$
$840$	−2.31136	−	9.26984i	−0.0797495	−	0.319840i
$841$	−10.8898	−	18.8618i	−0.375512	−	0.650406i
$842$	2.22657	−	3.85653i	0.0767326	−	0.132905i
$843$	5.77751	−	20.1496i	0.198988	−	0.693989i
$844$		−	15.0198i		−	0.517004i
$845$		0			0
$846$	1.56688	+	2.94669i	0.0538706	+	0.101309i
$847$	8.39923	−	2.25057i	0.288601	−	0.0773304i
$848$	6.97060	+	4.02448i	0.239371	+	0.138201i
$849$	−0.214628	+	12.3054i	−0.00736602	+	0.422319i
$850$	10.4067	+	10.4067i	0.356947	+	0.356947i
$851$	−5.65526	−	1.51532i	−0.193860	−	0.0519446i
$852$	−26.1966	−	27.1267i	−0.897482	−	0.929346i
$853$	−30.1644	+	30.1644i	−1.03281	+	1.03281i	−0.0333670	+	0.999443i	$0.510623\pi$
$853$	−30.1644	+	30.1644i	−1.03281	+	1.03281i	−0.999443	+	0.0333670i	$0.989377\pi$
$854$	0.944378	−	0.545237i	0.0323160	−	0.0186576i
$855$	51.3321	+	1.79120i	1.75552	+	0.0612577i
$856$	−4.61568	−	17.2259i	−0.157761	−	0.588771i
$857$	−36.7949			−1.25689			−0.628444	−	0.777855i	$-0.716308\pi$
$857$	−36.7949			−1.25689			−0.628444	+	0.777855i	$0.716308\pi$
$858$		0			0
$859$	−48.7044			−1.66177			−0.830886	−	0.556442i	$-0.812166\pi$
$859$	−48.7044			−1.66177			−0.830886	+	0.556442i	$0.812166\pi$
$860$	−9.36529	−	34.9518i	−0.319354	−	1.19185i
$861$	11.9809	−	6.64135i	0.408309	−	0.226336i
$862$	6.47872	−	3.74049i	0.220666	−	0.127402i
$863$	25.4155	−	25.4155i	0.865153	−	0.865153i	−0.126779	−	0.991931i	$-0.540464\pi$
$863$	25.4155	−	25.4155i	0.865153	−	0.865153i	0.991931	+	0.126779i	$0.0404637\pi$
$864$	−19.1970	−	6.23663i	−0.653094	−	0.212175i
$865$	47.8355	+	12.8175i	1.62646	+	0.435808i
$866$	−0.461976	−	0.461976i	−0.0156986	−	0.0156986i
$867$	−30.8772	−	0.538556i	−1.04864	−	0.0182903i
$868$	8.60919	+	4.97052i	0.292215	+	0.168710i
$869$	−1.99268	+	0.533937i	−0.0675971	+	0.0181126i
$870$	2.93571	−	4.88599i	0.0995299	−	0.165651i
$871$		0			0
$872$			8.67054i			0.293622i
$873$	25.1000	+	26.9150i	0.849505	+	0.910934i
$874$	−2.35262	+	4.07485i	−0.0795784	+	0.137834i
$875$	4.19056	+	7.25826i	0.141667	+	0.245374i
$876$	−40.7152	+	10.1520i	−1.37564	+	0.343005i
$877$	4.74247	−	17.6992i	0.160142	−	0.597658i	−0.838468	−	0.544951i	$-0.816548\pi$
$877$	4.74247	−	17.6992i	0.160142	−	0.597658i	0.998610	−	0.0527071i	$-0.0167850\pi$
$878$	−1.31404	+	4.90406i	−0.0443467	+	0.165504i
$879$	26.7130	−	6.66068i	0.901007	−	0.224659i
$880$	10.6551	+	18.4552i	0.359184	+	0.622125i
$881$	15.5539	−	26.9401i	0.524023	−	0.907635i	−0.475586	−	0.879669i	$-0.657764\pi$
$881$	15.5539	−	26.9401i	0.524023	−	0.907635i	0.999609	−	0.0279654i	$-0.00890283\pi$
$882$	4.07416	+	4.36877i	0.137184	+	0.147104i
$883$			9.56660i			0.321942i	0.986959	+	0.160971i	$0.0514625\pi$
$883$			9.56660i			0.321942i	−0.986959	+	0.160971i	$0.948537\pi$
$884$		0			0
$885$	−31.0229	+	51.6323i	−1.04282	+	1.73560i
$886$	7.56891	−	2.02808i	0.254282	−	0.0681348i
$887$	−21.3515	−	12.3273i	−0.716913	−	0.413910i	0.0967027	−	0.995313i	$-0.469170\pi$
$887$	−21.3515	−	12.3273i	−0.716913	−	0.413910i	−0.813615	+	0.581404i	$0.802504\pi$
$888$	−5.11141	−	0.0891524i	−0.171528	−	0.00299176i
$889$	6.40399	+	6.40399i	0.214783	+	0.214783i
$890$	−5.05616	−	1.35479i	−0.169483	−	0.0454128i
$891$	11.0734	+	12.7371i	0.370973	+	0.426710i
$892$	37.5558	−	37.5558i	1.25746	−	1.25746i
$893$	−13.4680	+	7.77574i	−0.450688	+	0.260205i
$894$	−12.1801	+	6.75173i	−0.407362	+	0.225812i
$895$	3.92737	+	14.6571i	0.131277	+	0.489934i
$896$	−11.1454			−0.372342
$897$		0			0
$898$	−8.66432			−0.289132
$899$	3.17189	+	11.8377i	0.105789	+	0.394808i
$900$	39.7926	+	1.38854i	1.32642	+	0.0462846i
$901$	−12.5800	+	7.26306i	−0.419100	+	0.241967i
$902$	3.18093	−	3.18093i	0.105913	−	0.105913i
$903$	−7.76123	−	8.03678i	−0.258278	−	0.267447i
$904$	17.1696	+	4.60057i	0.571051	+	0.153013i
$905$	−5.17824	−	5.17824i	−0.172130	−	0.172130i
$906$	−0.0996478	+	5.71314i	−0.00331058	+	0.189806i
$907$	−1.45939	−	0.842581i	−0.0484584	−	0.0279775i	0.475575	−	0.879675i	$-0.342240\pi$
$907$	−1.45939	−	0.842581i	−0.0484584	−	0.0279775i	−0.524033	+	0.851698i	$0.675573\pi$
$908$	−13.3266	+	3.57085i	−0.442259	+	0.118503i
$909$	15.6280	+	29.3900i	0.518346	+	0.974806i
$910$		0			0
$911$			43.9421i			1.45587i	0.685648	+	0.727933i	$0.259519\pi$
$911$			43.9421i			1.45587i	−0.685648	+	0.727933i	$0.740481\pi$
$912$	7.69167	−	26.8254i	0.254697	−	0.888277i
$913$	6.08545	−	10.5403i	0.201399	−	0.348834i
$914$	1.19283	+	2.06604i	0.0394553	+	0.0683386i
$915$	3.87734	+	15.5503i	0.128181	+	0.514076i
$916$	7.83348	−	29.2350i	0.258826	−	0.965950i
$917$	−5.57646	+	20.8116i	−0.184151	+	0.687260i
$918$	8.03165	−	7.23231i	0.265084	−	0.238702i
$919$	−4.20715	−	7.28699i	−0.138781	−	0.240376i	0.788254	−	0.615349i	$-0.210985\pi$
$919$	−4.20715	−	7.28699i	−0.138781	−	0.240376i	−0.927035	+	0.374974i	$0.877652\pi$
$920$	−6.43113	+	11.1390i	−0.212028	+	0.367243i
$921$	33.8700	+	9.71159i	1.11606	+	0.320008i
$922$			4.36704i			0.143821i
$923$		0			0
$924$	6.06857	+	3.64625i	0.199641	+	0.119953i
$925$	14.7674	−	3.95690i	0.485548	−	0.130102i
$926$	3.01029	+	1.73799i	0.0989244	+	0.0571140i
$927$	−11.2780	−	7.04686i	−0.370418	−	0.231449i
$928$	−7.38077	−	7.38077i	−0.242286	−	0.242286i
$929$	−2.21620	−	0.593828i	−0.0727110	−	0.0194829i	0.222280	−	0.974983i	$-0.428650\pi$
$929$	−2.21620	−	0.593828i	−0.0727110	−	0.0194829i	−0.294991	+	0.955500i	$0.595317\pi$
$930$	6.95951	−	6.72089i	0.228211	−	0.220387i
$931$	−19.6831	+	19.6831i	−0.645087	+	0.645087i
$932$	29.4930	−	17.0278i	0.966076	−	0.557764i
$933$	−6.40030	−	11.5461i	−0.209536	−	0.378002i
$934$	−0.839158	−	3.13178i	−0.0274581	−	0.102475i
$935$	−38.4590			−1.25775
$936$		0			0
$937$	7.10985			0.232269			0.116134	−	0.993234i	$-0.462950\pi$
$937$	7.10985			0.232269			0.116134	+	0.993234i	$0.462950\pi$
$938$	0.721146	+	2.69135i	0.0235463	+	0.0878758i
$939$	−5.47077	−	9.86922i	−0.178532	−	0.322070i
$940$	−17.8181	+	10.2873i	−0.581163	+	0.335534i
$941$	22.6506	−	22.6506i	0.738390	−	0.738390i	−0.233877	−	0.972266i	$-0.575141\pi$
$941$	22.6506	−	22.6506i	0.738390	−	0.738390i	0.972266	+	0.233877i	$0.0751412\pi$
$942$	−6.88469	+	6.64864i	−0.224315	+	0.216624i
$943$	−17.8142	−	4.77330i	−0.580110	−	0.155440i
$944$	23.1413	+	23.1413i	0.753185	+	0.753185i
$945$	18.6945	−	9.52623i	0.608131	−	0.309888i
$946$	−3.17745	−	1.83450i	−0.103308	−	0.0596448i
$947$	12.9169	−	3.46107i	0.419742	−	0.112470i	−0.0427648	−	0.999085i	$-0.513617\pi$
$947$	12.9169	−	3.46107i	0.419742	−	0.112470i	0.462507	+	0.886616i	$0.346950\pi$
$948$	3.06363	+	1.84076i	0.0995022	+	0.0597852i
$949$		0			0
$950$		−	12.2866i		−	0.398629i
$951$	−14.8203	−	4.24943i	−0.480580	−	0.137797i
$952$	4.68381	−	8.11259i	0.151803	−	0.262931i
$953$	8.89415	+	15.4051i	0.288110	+	0.499021i	0.973359	−	0.229288i	$-0.0736399\pi$
$953$	8.89415	+	15.4051i	0.288110	+	0.499021i	−0.685249	+	0.728309i	$0.740307\pi$
$954$	0.760824	−	2.48878i	0.0246326	−	0.0805772i
$955$	−6.11390	+	22.8174i	−0.197841	+	0.738353i
$956$	4.49206	−	16.7646i	0.145284	−	0.542206i
$957$	2.11157	+	8.46858i	0.0682575	+	0.273750i
$958$	−4.04423	−	7.00482i	−0.130663	−	0.226315i
$959$	4.37773	−	7.58246i	0.141364	−	0.244850i
$960$	8.57871	−	29.9190i	0.276877	−	0.965632i
$961$		−	10.1988i		−	0.328993i
$962$		0			0
$963$	34.5812	−	18.3883i	1.11436	−	0.592555i
$964$	−50.1473	+	13.4369i	−1.61513	+	0.432774i
$965$	−33.4536	−	19.3144i	−1.07691	−	0.621753i
$966$	−0.0335193	+	1.92177i	−0.00107847	+	0.0618321i
$967$	−29.0154	−	29.0154i	−0.933072	−	0.933072i	0.0648250	−	0.997897i	$-0.479351\pi$
$967$	−29.0154	−	29.0154i	−0.933072	−	0.933072i	−0.997897	+	0.0648250i	$0.979351\pi$
$968$	−9.87382	−	2.64568i	−0.317357	−	0.0850354i
$969$	34.9856	+	36.2277i	1.12390	+	1.16380i
$970$	10.6239	−	10.6239i	0.341114	−	0.341114i
$971$	19.5631	−	11.2948i	0.627810	−	0.362466i	−0.152093	−	0.988366i	$-0.548601\pi$
$971$	19.5631	−	11.2948i	0.627810	−	0.362466i	0.779904	+	0.625900i	$0.215268\pi$
$972$	2.54656	−	29.1295i	0.0816810	−	0.934328i
$973$	−1.62172	−	6.05235i	−0.0519900	−	0.194029i
$974$	−10.3864			−0.332803
$975$		0			0
$976$	8.70733			0.278715
$977$	−0.689868	−	2.57462i	−0.0220708	−	0.0823694i	0.954012	−	0.299768i	$-0.0969094\pi$
$977$	−0.689868	−	2.57462i	−0.0220708	−	0.0823694i	−0.976083	+	0.217399i	$0.930243\pi$
$978$	1.84540	−	1.02295i	0.0590092	−	0.0327104i
$979$	6.94116	−	4.00748i	0.221841	−	0.128080i
$980$	−26.0407	+	26.0407i	−0.831839	+	0.831839i
$981$	−18.5541	+	4.28406i	−0.592385	+	0.136779i
$982$	5.21679	+	1.39784i	0.166475	+	0.0446067i
$983$	−38.5049	−	38.5049i	−1.22812	−	1.22812i	−0.964676	−	0.263440i	$-0.915143\pi$
$983$	−38.5049	−	38.5049i	−1.22812	−	1.22812i	−0.263440	−	0.964676i	$-0.584857\pi$
$984$	−16.1010	−	0.280832i	−0.513282	−	0.00895260i
$985$	6.87308	+	3.96818i	0.218995	+	0.126437i
$986$	5.39867	−	1.44657i	0.171929	−	0.0460682i
$987$	−3.27182	+	5.44538i	−0.104143	+	0.173328i
$988$		0			0
$989$			15.0419i			0.478303i
$990$	5.03909	−	4.69928i	0.160153	−	0.149353i
$991$	−6.62217	+	11.4699i	−0.210360	+	0.364354i	−0.951827	−	0.306635i	$-0.900797\pi$
$991$	−6.62217	+	11.4699i	−0.210360	+	0.364354i	0.741467	+	0.670989i	$0.234130\pi$
$992$	−8.85836	−	15.3431i	−0.281253	−	0.487145i
$993$	−27.0183	+	6.73680i	−0.857400	+	0.213786i
$994$	−1.23032	+	4.59160i	−0.0390232	+	0.145637i
$995$	−16.4977	+	61.5704i	−0.523013	+	1.95191i
$996$	−20.4597	+	5.10147i	−0.648291	+	0.161646i
$997$	15.7906	+	27.3501i	0.500093	+	0.866186i	1.00000		0.000107105i	$3.40926e-5\pi$
$997$	15.7906	+	27.3501i	0.500093	+	0.866186i	−0.499907	+	0.866079i	$0.666633\pi$
$998$	−7.36014	+	12.7481i	−0.232981	+	0.403535i
$999$	−2.33473	−	10.9819i	−0.0738677	−	0.347453i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.k.k.488.14		96
3.2	odd	2	inner	507.2.k.k.488.11		96
13.2	odd	12	inner	507.2.k.k.80.11		96
13.3	even	3	inner	507.2.k.k.89.11		96
13.4	even	6		507.2.f.g.437.11	yes	48
13.5	odd	4	inner	507.2.k.k.188.14		96
13.6	odd	12		507.2.f.g.239.11	✓	48
13.7	odd	12		507.2.f.g.239.13	yes	48
13.8	odd	4	inner	507.2.k.k.188.12		96
13.9	even	3		507.2.f.g.437.13	yes	48
13.10	even	6	inner	507.2.k.k.89.13		96
13.11	odd	12	inner	507.2.k.k.80.13		96
13.12	even	2	inner	507.2.k.k.488.12		96
39.2	even	12	inner	507.2.k.k.80.14		96
39.5	even	4	inner	507.2.k.k.188.11		96
39.8	even	4	inner	507.2.k.k.188.13		96
39.11	even	12	inner	507.2.k.k.80.12		96
39.17	odd	6		507.2.f.g.437.14	yes	48
39.20	even	12		507.2.f.g.239.12	yes	48
39.23	odd	6	inner	507.2.k.k.89.12		96
39.29	odd	6	inner	507.2.k.k.89.14		96
39.32	even	12		507.2.f.g.239.14	yes	48
39.35	odd	6		507.2.f.g.437.12	yes	48
39.38	odd	2	inner	507.2.k.k.488.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.11	✓	48	13.6	odd	12
507.2.f.g.239.12	yes	48	39.20	even	12
507.2.f.g.239.13	yes	48	13.7	odd	12
507.2.f.g.239.14	yes	48	39.32	even	12
507.2.f.g.437.11	yes	48	13.4	even	6
507.2.f.g.437.12	yes	48	39.35	odd	6
507.2.f.g.437.13	yes	48	13.9	even	3
507.2.f.g.437.14	yes	48	39.17	odd	6
507.2.k.k.80.11		96	13.2	odd	12	inner
507.2.k.k.80.12		96	39.11	even	12	inner
507.2.k.k.80.13		96	13.11	odd	12	inner
507.2.k.k.80.14		96	39.2	even	12	inner
507.2.k.k.89.11		96	13.3	even	3	inner
507.2.k.k.89.12		96	39.23	odd	6	inner
507.2.k.k.89.13		96	13.10	even	6	inner
507.2.k.k.89.14		96	39.29	odd	6	inner
507.2.k.k.188.11		96	39.5	even	4	inner
507.2.k.k.188.12		96	13.8	odd	4	inner
507.2.k.k.188.13		96	39.8	even	4	inner
507.2.k.k.188.14		96	13.5	odd	4	inner
507.2.k.k.488.11		96	3.2	odd	2	inner
507.2.k.k.488.12		96	13.12	even	2	inner
507.2.k.k.488.13		96	39.38	odd	2	inner
507.2.k.k.488.14		96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.k (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0912193 + 0.340435i) q^{2} +(0.839735 + 1.51487i) q^{3} +(1.62448 - 0.937892i) q^{4} +(2.45719 - 2.45719i) q^{5} +(-0.439116 + 0.424061i) q^{6} +(-1.12240 - 0.300747i) q^{7} +(0.965906 + 0.965906i) q^{8} +(-1.58969 + 2.54419i) q^{9} +(1.06066 + 0.612371i) q^{10} +(-1.81140 + 0.485362i) q^{11} +(2.78492 + 1.67330i) q^{12} -0.409539i q^{14} +(5.78573 + 1.65895i) q^{15} +(1.63506 - 2.83201i) q^{16} +(2.95083 + 5.11099i) q^{17} +(-1.01114 - 0.309108i) q^{18} +(1.27519 - 4.75906i) q^{19} +(1.68707 - 6.29623i) q^{20} +(-0.486926 - 1.95284i) q^{21} +(-0.330468 - 0.572388i) q^{22} +(-1.35482 + 2.34662i) q^{23} +(-0.652122 + 2.27433i) q^{24} -7.07560i q^{25} +(-5.18904 - 0.271740i) q^{27} +(-2.10538 + 0.564135i) q^{28} +(-2.32707 - 1.34353i) q^{29} +(-0.0369941 + 2.12099i) q^{30} +(-3.22500 - 3.22500i) q^{31} +(3.75217 + 1.00539i) q^{32} +(-2.25635 - 2.33646i) q^{33} +(-1.47079 + 1.47079i) q^{34} +(-3.49695 + 2.01896i) q^{35} +(-0.196243 + 5.62393i) q^{36} +(0.559232 + 2.08708i) q^{37} +1.73647 q^{38} +4.74684 q^{40} +(1.76159 + 6.57436i) q^{41} +(0.620400 - 0.343904i) q^{42} +(4.80750 - 2.77561i) q^{43} +(-2.48735 + 2.48735i) q^{44} +(2.34538 + 10.1577i) q^{45} +(-0.922459 - 0.247172i) q^{46} +(-2.23192 - 2.23192i) q^{47} +(5.66317 + 0.0987761i) q^{48} +(-4.89284 - 2.82488i) q^{49} +(2.40878 - 0.645431i) q^{50} +(-5.26460 + 8.76202i) q^{51} +2.46136i q^{53} +(-0.380831 - 1.79132i) q^{54} +(-3.25832 + 5.64358i) q^{55} +(-0.793642 - 1.37463i) q^{56} +(8.28020 - 2.06460i) q^{57} +(0.245112 - 0.914771i) q^{58} +(-2.59020 + 9.66677i) q^{59} +(10.9547 - 2.73147i) q^{60} +(1.33134 + 2.30596i) q^{61} +(0.803720 - 1.39208i) q^{62} +(2.54943 - 2.37750i) q^{63} -5.17117i q^{64} +(0.589590 - 0.981273i) q^{66} +(-6.57167 + 1.76087i) q^{67} +(9.58711 + 5.53512i) q^{68} +(-4.69254 - 0.0818465i) q^{69} +(-1.00632 - 1.00632i) q^{70} +(-11.2116 - 3.00415i) q^{71} +(-3.99294 + 0.921953i) q^{72} +(-9.13263 + 9.13263i) q^{73} +(-0.659503 + 0.380764i) q^{74} +(10.7186 - 5.94163i) q^{75} +(-2.39197 - 8.92696i) q^{76} +2.17908 q^{77} +1.10008 q^{79} +(-2.94114 - 10.9765i) q^{80} +(-3.94577 - 8.08894i) q^{81} +(-2.07745 + 1.19942i) q^{82} +(-4.58922 + 4.58922i) q^{83} +(-2.62256 - 2.71567i) q^{84} +(19.8095 + 5.30793i) q^{85} +(1.38345 + 1.38345i) q^{86} +(0.0811644 - 4.65342i) q^{87} +(-2.21845 - 1.28082i) q^{88} +(-4.12834 + 1.10619i) q^{89} +(-3.24410 + 1.72503i) q^{90} +5.08271i q^{92} +(2.17732 - 7.59361i) q^{93} +(0.556230 - 0.963419i) q^{94} +(-8.56055 - 14.8273i) q^{95} +(1.62779 + 6.52833i) q^{96} +(3.17506 - 11.8495i) q^{97} +(0.515368 - 1.92338i) q^{98} +(1.64471 - 5.38010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{9} + 8 q^{16} - 112 q^{22} - 168 q^{27} + 256 q^{40} + 56 q^{42} + 188 q^{48} - 8 q^{55} - 56 q^{61} - 184 q^{66} + 72 q^{81} + 112 q^{87} - 296 q^{94}+O(q^{100}) \) 96 * q + 24 * q^9 + 8 * q^16 - 112 * q^22 - 168 * q^27 + 256 * q^40 + 56 * q^42 + 188 * q^48 - 8 * q^55 - 56 * q^61 - 184 * q^66 + 72 * q^81 + 112 * q^87 - 296 * q^94

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